# Classes¶

## Qobj¶

class Qobj(inpt=None, dims=None, shape=None, type=None, isherm=None, copy=True, fast=False, superrep=None, isunitary=None)[source]

A class for representing quantum objects, such as quantum operators and states.

The Qobj class is the QuTiP representation of quantum operators and state vectors. This class also implements math operations +,-,* between Qobj instances (and / by a C-number), as well as a collection of common operator/state operations. The Qobj constructor optionally takes a dimension list and/or shape list as arguments.

Parameters
inptarray_like

Data for vector/matrix representation of the quantum object.

dimslist

Dimensions of object used for tensor products.

shapelist

Shape of underlying data structure (matrix shape).

copybool

Flag specifying whether Qobj should get a copy of the input data, or use the original.

fastbool

Flag for fast qobj creation when running ode solvers. This parameter is used internally only.

Attributes
dataarray_like

Sparse matrix characterizing the quantum object.

dimslist

List of dimensions keeping track of the tensor structure.

shapelist

Shape of the underlying data array.

typestr

Type of quantum object: ‘bra’, ‘ket’, ‘oper’, ‘operator-ket’, ‘operator-bra’, or ‘super’.

superrepstr

Representation used if type is ‘super’. One of ‘super’ (Liouville form) or ‘choi’ (Choi matrix with tr = dimension).

ishermbool

Indicates if quantum object represents Hermitian operator.

isunitarybool

Indictaes if quantum object represents unitary operator.

iscpbool

Indicates if the quantum object represents a map, and if that map is completely positive (CP).

ishpbool

Indicates if the quantum object represents a map, and if that map is hermicity preserving (HP).

istpbool

Indicates if the quantum object represents a map, and if that map is trace preserving (TP).

iscptpbool

Indicates if the quantum object represents a map that is completely positive and trace preserving (CPTP).

isketbool

Indicates if the quantum object represents a ket.

isbrabool

Indicates if the quantum object represents a bra.

isoperbool

Indicates if the quantum object represents an operator.

issuperbool

Indicates if the quantum object represents a superoperator.

isoperketbool

Indicates if the quantum object represents an operator in column vector form.

isoperbrabool

Indicates if the quantum object represents an operator in row vector form.

Methods

 copy() Create copy of Qobj conj() Conjugate of quantum object. cosm() Cosine of quantum object. dag() Adjoint (dagger) of quantum object. dnorm() Diamond norm of quantum operator. dual_chan() Dual channel of quantum object representing a CP map. eigenenergies(sparse=False, sort=’low’, eigvals=0, tol=0, maxiter=100000) Returns eigenenergies (eigenvalues) of a quantum object. eigenstates(sparse=False, sort=’low’, eigvals=0, tol=0, maxiter=100000) Returns eigenenergies and eigenstates of quantum object. expm() Matrix exponential of quantum object. full(order=’C’) Returns dense array of quantum object data attribute. groundstate(sparse=False, tol=0, maxiter=100000) Returns eigenvalue and eigenket for the groundstate of a quantum object. inv() Return a Qobj corresponding to the matrix inverse of the operator. matrix_element(bra, ket) Returns the matrix element of operator between bra and ket vectors. norm(norm=’tr’, sparse=False, tol=0, maxiter=100000) Returns norm of a ket or an operator. permute(order) Returns composite qobj with indices reordered. proj() Computes the projector for a ket or bra vector. ptrace(sel) Returns quantum object for selected dimensions after performing partial trace. sinm() Sine of quantum object. sqrtm() Matrix square root of quantum object. tidyup(atol=1e-12) Removes small elements from quantum object. tr() Trace of quantum object. trans() Transpose of quantum object. transform(inpt, inverse=False) Performs a basis transformation defined by inpt matrix. trunc_neg(method=’clip’) Removes negative eigenvalues and returns a new Qobj that is a valid density operator. unit(norm=’tr’, sparse=False, tol=0, maxiter=100000) Returns normalized quantum object.
check_herm()[source]

Check if the quantum object is hermitian.

Returns
ishermbool

Returns the new value of isherm property.

check_isunitary()[source]

Checks whether qobj is a unitary matrix

conj()[source]

Conjugate operator of quantum object.

copy()[source]

Create identical copy

cosm()[source]

Cosine of a quantum operator.

Operator must be square.

Returns
operqutip.Qobj

Matrix cosine of operator.

Raises
TypeError

Quantum object is not square.

Notes

Uses the Q.expm() method.

dag()[source]

diag()[source]

Diagonal elements of quantum object.

Returns
diagsarray

Returns array of real values if operators is Hermitian, otherwise complex values are returned.

dnorm(B=None)[source]

Calculates the diamond norm, or the diamond distance to another operator.

Parameters
Bqutip.Qobj or None

If B is not None, the diamond distance d(A, B) = dnorm(A - B) between this operator and B is returned instead of the diamond norm.

Returns
dfloat

Either the diamond norm of this operator, or the diamond distance from this operator to B.

dual_chan()[source]

Dual channel of quantum object representing a completely positive map.

eigenenergies(sparse=False, sort='low', eigvals=0, tol=0, maxiter=100000)[source]

Eigenenergies of a quantum object.

Eigenenergies (eigenvalues) are defined for operators or superoperators only.

Parameters
sparsebool

Use sparse Eigensolver

sortstr

Sort eigenvalues ‘low’ to high, or ‘high’ to low.

eigvalsint

Number of requested eigenvalues. Default is all eigenvalues.

tolfloat

Tolerance used by sparse Eigensolver (0=machine precision). The sparse solver may not converge if the tolerance is set too low.

maxiterint

Maximum number of iterations performed by sparse solver (if used).

Returns
eigvalsarray

Array of eigenvalues for operator.

Notes

The sparse eigensolver is much slower than the dense version. Use sparse only if memory requirements demand it.

eigenstates(sparse=False, sort='low', eigvals=0, tol=0, maxiter=100000, phase_fix=None)[source]

Eigenstates and eigenenergies.

Eigenstates and eigenenergies are defined for operators and superoperators only.

Parameters
sparsebool

Use sparse Eigensolver

sortstr

Sort eigenvalues (and vectors) ‘low’ to high, or ‘high’ to low.

eigvalsint

Number of requested eigenvalues. Default is all eigenvalues.

tolfloat

Tolerance used by sparse Eigensolver (0 = machine precision). The sparse solver may not converge if the tolerance is set too low.

maxiterint

Maximum number of iterations performed by sparse solver (if used).

phase_fixint, None

If not None, set the phase of each kets so that ket[phase_fix,0] is real positive.

Returns
eigvalsarray

Array of eigenvalues for operator.

eigvecsarray

Array of quantum operators representing the oprator eigenkets. Order of eigenkets is determined by order of eigenvalues.

Notes

The sparse eigensolver is much slower than the dense version. Use sparse only if memory requirements demand it.

eliminate_states(states_inds, normalize=False)[source]

Creates a new quantum object with states in state_inds eliminated.

Parameters
states_indslist of integer

The states that should be removed.

normalizeTrue / False

Weather or not the new Qobj instance should be normalized (default is False). For Qobjs that represents density matrices or state vectors normalized should probably be set to True, but for Qobjs that represents operators in for example an Hamiltonian, normalize should be False.

Returns
qqutip.Qobj

A new instance of qutip.Qobj that contains only the states corresponding to indices that are not in state_inds.

Notes

Experimental.

static evaluate(qobj_list, t, args)[source]

Evaluate a time-dependent quantum object in list format. For example,

qobj_list = [H0, [H1, func_t]]

is evaluated to

Qobj(t) = H0 + H1 * func_t(t, args)

and

qobj_list = [H0, [H1, ‘sin(w * t)’]]

is evaluated to

Qobj(t) = H0 + H1 * sin(args[‘w’] * t)

Parameters
qobj_listlist

A nested list of Qobj instances and corresponding time-dependent coefficients.

tfloat

The time for which to evaluate the time-dependent Qobj instance.

argsdictionary

A dictionary with parameter values required to evaluate the time-dependent Qobj intance.

Returns
outputqutip.Qobj

A Qobj instance that represents the value of qobj_list at time t.

expm(method='dense')[source]

Matrix exponential of quantum operator.

Input operator must be square.

Parameters
methodstr {‘dense’, ‘sparse’}

Use set method to use to calculate the matrix exponentiation. The available choices includes ‘dense’ and ‘sparse’. Since the exponential of a matrix is nearly always dense, method=’dense’ is set as default.s

Returns
operqutip.Qobj

Exponentiated quantum operator.

Raises
TypeError

Quantum operator is not square.

extract_states(states_inds, normalize=False)[source]

Qobj with states in state_inds only.

Parameters
states_indslist of integer

The states that should be kept.

normalizeTrue / False

Weather or not the new Qobj instance should be normalized (default is False). For Qobjs that represents density matrices or state vectors normalized should probably be set to True, but for Qobjs that represents operators in for example an Hamiltonian, normalize should be False.

Returns
qqutip.Qobj

A new instance of qutip.Qobj that contains only the states corresponding to the indices in state_inds.

Notes

Experimental.

full(order='C', squeeze=False)[source]

Dense array from quantum object.

Parameters
orderstr {‘C’, ‘F’}

Return array in C (default) or Fortran ordering.

squeezebool {False, True}

Squeeze output array.

Returns
dataarray

Array of complex data from quantum objects data attribute.

groundstate(sparse=False, tol=0, maxiter=100000, safe=True)[source]

Ground state Eigenvalue and Eigenvector.

Defined for quantum operators or superoperators only.

Parameters
sparsebool

Use sparse Eigensolver

tolfloat

Tolerance used by sparse Eigensolver (0 = machine precision). The sparse solver may not converge if the tolerance is set too low.

maxiterint

Maximum number of iterations performed by sparse solver (if used).

safebool (default=True)

Check for degenerate ground state

Returns
eigvalfloat

Eigenvalue for the ground state of quantum operator.

eigvecqutip.Qobj

Eigenket for the ground state of quantum operator.

Notes

The sparse eigensolver is much slower than the dense version. Use sparse only if memory requirements demand it.

inv(sparse=False)[source]

Matrix inverse of a quantum operator

Operator must be square.

Returns
operqutip.Qobj

Matrix inverse of operator.

Raises
TypeError

Quantum object is not square.

matrix_element(bra, ket)[source]

Calculates a matrix element.

Gives the matrix element for the quantum object sandwiched between a bra and ket vector.

Parameters
braqutip.Qobj

Quantum object of type ‘bra’ or ‘ket’

ketqutip.Qobj

Quantum object of type ‘ket’.

Returns
elemcomplex

Complex valued matrix element.

Notes

It is slightly more computationally efficient to use a ket vector for the ‘bra’ input.

norm(norm=None, sparse=False, tol=0, maxiter=100000)[source]

Norm of a quantum object.

Default norm is L2-norm for kets and trace-norm for operators. Other ket and operator norms may be specified using the norm and argument.

Parameters
normstr

Which norm to use for ket/bra vectors: L2 ‘l2’, max norm ‘max’, or for operators: trace ‘tr’, Frobius ‘fro’, one ‘one’, or max ‘max’.

sparsebool

Use sparse eigenvalue solver for trace norm. Other norms are not affected by this parameter.

tolfloat

Tolerance for sparse solver (if used) for trace norm. The sparse solver may not converge if the tolerance is set too low.

maxiterint

Maximum number of iterations performed by sparse solver (if used) for trace norm.

Returns
normfloat

The requested norm of the operator or state quantum object.

Notes

The sparse eigensolver is much slower than the dense version. Use sparse only if memory requirements demand it.

overlap(other)[source]

Overlap between two state vectors or two operators.

Gives the overlap (inner product) between the current bra or ket Qobj and and another bra or ket Qobj. It gives the Hilbert-Schmidt overlap when one of the Qobj is an operator/density matrix.

Parameters
otherqutip.Qobj

Quantum object for a state vector of type ‘ket’, ‘bra’ or density matrix.

Returns
overlapcomplex

Complex valued overlap.

Raises
TypeError

Can only calculate overlap between a bra, ket and density matrix quantum objects.

Notes

Since QuTiP mainly deals with ket vectors, the most efficient inner product call is the ket-ket version that computes the product <self|other> with both vectors expressed as kets.

permute(order)[source]

Permutes a composite quantum object.

Parameters
orderlist/array

List specifying new tensor order.

Returns
Pqutip.Qobj

Permuted quantum object.

proj()[source]

Form the projector from a given ket or bra vector.

Parameters
Qqutip.Qobj

Input bra or ket vector

Returns
Pqutip.Qobj

Projection operator.

ptrace(sel, sparse=None)[source]

Partial trace of the quantum object.

Parameters
selint/list

An int or list of components to keep after partial trace. The order is unimportant; no transposition will be done and the spaces will remain in the same order in the output.

Returns
operqutip.Qobj

Quantum object representing partial trace with selected components remaining.

Notes

This function is identical to the qutip.qobj.ptrace function that has been deprecated.

purity()[source]

Calculate purity of a quantum object.

Returns
state_purityfloat

Returns the purity of a quantum object. For a pure state, the purity is 1. For a mixed state of dimension d, 1/d<=purity<1.

sinm()[source]

Sine of a quantum operator.

Operator must be square.

Returns
operqutip.Qobj

Matrix sine of operator.

Raises
TypeError

Quantum object is not square.

Notes

Uses the Q.expm() method.

sqrtm(sparse=False, tol=0, maxiter=100000)[source]

Sqrt of a quantum operator.

Operator must be square.

Parameters
sparsebool

Use sparse eigenvalue/vector solver.

tolfloat

Tolerance used by sparse solver (0 = machine precision).

maxiterint

Maximum number of iterations used by sparse solver.

Returns
operqutip.Qobj

Matrix square root of operator.

Raises
TypeError

Quantum object is not square.

Notes

The sparse eigensolver is much slower than the dense version. Use sparse only if memory requirements demand it.

tidyup(atol=1e-12)[source]

Removes small elements from the quantum object.

Parameters
atolfloat

Absolute tolerance used by tidyup. Default is set via qutip global settings parameters.

Returns
operqutip.Qobj

Quantum object with small elements removed.

tr()[source]

Trace of a quantum object.

Returns
tracefloat

Returns the trace of the quantum object.

trans()[source]

Transposed operator.

Returns
operqutip.Qobj

Transpose of input operator.

transform(inpt, inverse=False, sparse=True)[source]

Basis transform defined by input array.

Input array can be a matrix defining the transformation, or a list of kets that defines the new basis.

Parameters
inptarray_like

A matrix or list of kets defining the transformation.

inversebool

Whether to return inverse transformation.

sparsebool

Use sparse matrices when possible. Can be slower.

Returns
operqutip.Qobj

Operator in new basis.

Notes

This function is still in development.

trunc_neg(method='clip')[source]

Truncates negative eigenvalues and renormalizes.

Returns a new Qobj by removing the negative eigenvalues of this instance, then renormalizing to obtain a valid density operator.

Parameters
methodstr

Algorithm to use to remove negative eigenvalues. “clip” simply discards negative eigenvalues, then renormalizes. “sgs” uses the SGS algorithm (doi:10/bb76) to find the positive operator that is nearest in the Shatten 2-norm.

Returns
operqutip.Qobj

A valid density operator.

unit(inplace=False, norm=None, sparse=False, tol=0, maxiter=100000)[source]

Operator or state normalized to unity.

Uses norm from Qobj.norm().

Parameters
inplacebool

Do an in-place normalization

normstr

Requested norm for states / operators.

sparsebool

Use sparse eigensolver for trace norm. Does not affect other norms.

tolfloat

Tolerance used by sparse eigensolver.

maxiterint

Number of maximum iterations performed by sparse eigensolver.

Returns
operqutip.Qobj

Normalized quantum object if not in-place, else None.

## QobjEvo¶

class QobjEvo(Q_object=[], args={}, copy=True, tlist=None, state0=None, e_ops=[])[source]

A class for representing time-dependent quantum objects, such as quantum operators and states.

Basic math operations are defined:

This object is constructed by passing a list of Qobj instances, each of which may have an associated scalar time dependence. The list is summed to produce the final result. In other words, if an instance of this class is $$Q(t)$$, then it is constructed from a set of constant Qobj $$\{Q_k\}$$ and time-dependent scalars $$f_k(t)$$ by

$Q(t) = \sum_k f_k(t) Q_k$

If a scalar $$f_k(t)$$ is not passed with a given Qobj, then that term is assumed to be constant. The next section contains more detail on the allowed forms of the constants, and gives several examples for how to build instances of this class.

Time-dependence formats

There are three major formats for specifying a time-dependent scalar:

• Python function

• string

• array

For function format, the function signature must be f(t: float, args: dict) -> complex, for example

def f1_t(t, args):
return np.exp(-1j * t * args["w1"])

def f2_t(t, args):
return np.cos(t * args["w2"])

H = QobjEvo([H0, [H1, f1_t], [H2, f2_t]], args={"w1":1., "w2":2.})


For string-based coeffients, the string must be a compilable python code resulting in a complex. The following symbols are defined:

pi   exp   log   log10
erf  zerf  norm  proj
real imag conj abs arg
sin  sinh  asin  asinh
cos  cosh  acos  acosh
tan  tanh  atan  atanh
numpy as np
scipy.special as spe


A couple more simple examples:

H = QobjEvo([H0, [H1, 'exp(-1j*w1*t)'], [H2, 'cos(w2*t)']],
args={"w1":1.,"w2":2.})


For numpy array format, the array must be an 1d of dtype np.float64 or np.complex128. A list of times (np.float64) at which the coeffients must be given as tlist. The coeffients array must have the same length as the tlist. The times of the tlist do not need to be equidistant, but must be sorted. By default, a cubic spline interpolation will be used for the coefficient at time t. If the coefficients are to be treated as step functions, use the arguments args = {"_step_func_coeff": True}. Examples of array-format usage are:

tlist = np.logspace(-5,0,100)
H = QobjEvo([H0, [H1, np.exp(-1j*tlist)], [H2, np.cos(2.*tlist)]],
tlist=tlist)


Mixing time formats is allowed. It is not possible to create a single QobjEvo that contains different tlist values, however.

Passing arguments

args is a dict of (name: object). The name must be a valid Python identifier string, and in general the object can be any type that is supported by the code to be compiled in the string.

There are some “magic” names that can be specified, whose objects will be overwritten when used within sesolve, mesolve and mcsolve. This allows access to the solvers’ internal states, and they are updated at every call. The initial values of these dictionary elements is unimportant. The magic names available are:

• "state": the current state as a Qobj

• "state_vec": the current state as a column-stacked 1D np.ndarray

• "state_mat": the current state as a 2D np.ndarray

• "expect_op_<n>": the current expectation value of the element e_ops[n], which is an argument to the solvers. Replace <n> with an integer literal, e.g. "expect_op_0". This will be either real- or complex-valued, depending on whether the state and operator are both Hermitian or not.

• "collapse": (mcsolve only) a list of the collapses that have occurred during the evolution. Each element of the list is a 2-tuple (time: float, which: int), where time is the time this collapse happened, and which is an integer indexing the c_ops argument to mcsolve.

Parameters
Q_object

The time-dependent description of the quantum object. This is of the same format as the first parameter to the general ODE solvers; in general, it is a list of [Qobj, time_dependence] pairs that are summed to make the whole object. The time_dependence can be any of the formats discussed in the previous section. If a particular term has no time-dependence, then you should just give the Qobj instead of the 2-element list.

argsdict, optional

Mapping of {str: object}, discussed in greater detail above. The strings can be any valid Python identifier, and the objects are of the consumable types. See the previous section for details on the “magic” names used to access solver internals.

tlistarray_like, optional

List of the times any numpy-array coefficients describe. This is used only in at least one of the time dependences in Q_object is given in Numpy-array format. The times must be sorted, but need not be equidistant. Values inbetween will be interpolated.

Attributes
cteQobj

Constant part of the QobjEvo.

opslist of EvoElement

Internal representation of the time-dependence structure of the elements.

argsdict

The current value of the args dictionary passed into the constructor.

dynamics_argslist

Names of the dynamic arguments that the solvers will generate. These are the magic names that were found in the args parameter.

tlistarray_like

List of times at which the numpy-array coefficients are applied.

compiledstr

A string representing the properties of the low-level Cython class backing this object (may be empty).

compiled_qobjevoCQobjCte or CQobjEvoTd

Cython version of the QobjEvo.

coeff_getcallable

Object called to obtain a list of all the coefficients at a particular time.

coeff_fileslist

Runtime created files to delete with the instance.

dummy_ctebool

Is self.cte an empty Qobj

constbool

Indicates if quantum object is constant

type{“cte”, “string”, “func”, “array”, “spline”, “mixed_callable”, “mixed_compilable”}

Information about the type of coefficients used in the entire object.

num_objint

Number of Qobj in the QobjEvo.

use_cythonbool

Flag to compile string to Cython or Python

safePicklebool

Flag to not share pointers between thread.

apply(function, *args, **kw_args)[source]

Apply the linear function function to every Qobj included in this time-dependent object, and return a new QobjEvo with the result.

Any additional arguments or keyword arguments will be appended to every function call.

apply_decorator(function, *args, str_mod=None, inplace_np=False, **kw_args)[source]

Apply the given function to every time-dependent coefficient in the quantum object, and return a new object with the result.

Any additional arguments and keyword arguments will be appended to the function calls.

Parameters
functioncallable

(time_dependence, *args, **kwargs) -> time_dependence. Called on each time-dependent coefficient to produce a new coefficient. The additional arguments and keyword arguments are the ones given to this function.

str_modlist

A 2-element list of strings, that will additionally wrap any string time-dependences. An existing time-dependence string x will become str_mod[0] + x + str_mod[1].

inplace_npbool, default False

Whether this function should modify Numpy arrays inplace, or be used like a regular decorator. Some decorators create incorrect arrays as some transformations f'(t) = f(g(t)) create a mismatch between the array and the associated time list.

arguments(new_args)[source]

Update the scoped variables that were passed as args to new values.

compile(code=False, matched=False, dense=False, omp=0)[source]

Create an associated Cython object for faster usage. This function is called automatically by the solvers.

Parameters
codebool, default False

Return the code string generated by compilation of any strings.

matchedbool, default False

If True, the underlying sparse matrices used to represent each element of the type will have their structures unified. This may include adding explicit zeros to sparse matrices, but can be faster in some cases due to not having to deal with repeated structural mismatches.

densebool, default False

Whether to swap to using dense matrices to back the data.

ompint, optional

The number of OpenMP threads to use when doing matrix multiplications, if QuTiP was compiled with OpenMP.

Returns
compiled_strstr

(Only if code was set to True). The code-generated string of compiled calling code.

compress()[source]

Merge together elements that share the same time-dependence, to reduce the number of matrix multiplications and additions that need to be done to evaluate this object.

Modifies the object inplace.

conj()[source]

Return the matrix elementwise conjugation.

copy()[source]

Return a copy of this object.

dag()[source]

Return the matrix conjugate-transpose (dagger).

expect(t, state, herm=False)[source]

Calculate the expectation value of this operator on the given (time-independent) state at a particular time.

This is more efficient than expect(QobjEvo(t), state).

Parameters
tfloat

The time to evaluate this operator at.

stateQobj or np.ndarray

The state to take the expectation value around.

hermbool, default False

Whether this operator and the state are both Hermitian. If True, only the real part of the result will be returned.

expect

General-purpose expectation values.

mul_mat(t, mat)[source]

Multiply this object evaluated at time t by a matrix (from the right).

Parameters
tfloat

The time to evaluate this object at.

matQobj or np.ndarray

The matrix that is multiplied by this object.

Returns
mat: Qobj or np.ndarray

The matrix result in the same type as the input.

mul_vec(t, vec)[source]

Multiply this object evaluated at time t by a vector.

Parameters
tfloat

The time to evaluate this object at.

vecQobj or np.ndarray

The state-vector to multiply this object by.

Returns
vec: Qobj or np.ndarray

The vector result in the same type as the input.

permute(order)[source]

Permute the tensor structure of the underlying matrices into a new format.

Qobj.permute

the same operation on constant quantum objects.

tidyup(atol=1e-12)[source]

Removes small elements from this quantum object inplace.

to_list()[source]

Return this operator in the list-like form used to initialised it, like can be passed to mesolve.

trans()[source]

Return the matrix transpose.

## eseries¶

class eseries(q=None, s=array([], dtype=float64))[source]

Class representation of an exponential-series expansion of time-dependent quantum objects.

Deprecated since version 4.6.0: eseries will be removed in QuTiP 5. Please use QobjEvo for general time-dependence.

Attributes
amplndarray

Array of amplitudes for exponential series.

ratesndarray

Array of rates for exponential series.

dimslist

Dimensions of exponential series components

shapelist

Shape corresponding to exponential series components

Methods

 value(tlist) Evaluate an exponential series at the times listed in tlist spec(wlist) Evaluate the spectrum of an exponential series at frequencies in wlist. tidyup() Returns a tidier version of the exponential series
spec(wlist)[source]

Evaluate the spectrum of an exponential series at frequencies in wlist.

Parameters
wlistarray_like

Array/list of frequenies.

Returns
val_listndarray

Values of exponential series at frequencies in wlist.

tidyup(*args)[source]

Returns a tidier version of exponential series.

value(tlist)[source]

Evaluates an exponential series at the times listed in tlist.

Parameters
tlistndarray

Times at which to evaluate exponential series.

Returns
val_listndarray

Values of exponential at times in tlist.

## Bloch sphere¶

class Bloch(fig=None, axes=None, view=None, figsize=None, background=False)[source]

Class for plotting data on the Bloch sphere. Valid data can be either points, vectors, or Qobj objects.

Attributes
axesmatplotlib.axes.Axes

User supplied Matplotlib axes for Bloch sphere animation.

figmatplotlib.figure.Figure

User supplied Matplotlib Figure instance for plotting Bloch sphere.

font_colorstr, default ‘black’

Color of font used for Bloch sphere labels.

font_sizeint, default 20

Size of font used for Bloch sphere labels.

frame_alphafloat, default 0.1

Sets transparency of Bloch sphere frame.

frame_colorstr, default ‘gray’

Color of sphere wireframe.

frame_widthint, default 1

Width of wireframe.

point_colorlist, default [“b”, “r”, “g”, “#CC6600”]

List of colors for Bloch sphere point markers to cycle through, i.e. by default, points 0 and 4 will both be blue (‘b’).

point_markerlist, default [“o”, “s”, “d”, “^”]

List of point marker shapes to cycle through.

point_sizelist, default [25, 32, 35, 45]

List of point marker sizes. Note, not all point markers look the same size when plotted!

sphere_alphafloat, default 0.2

Transparency of Bloch sphere itself.

sphere_colorstr, default ‘#FFDDDD’

Color of Bloch sphere.

figsizelist, default [7, 7]

Figure size of Bloch sphere plot. Best to have both numbers the same; otherwise you will have a Bloch sphere that looks like a football.

vector_colorlist, [“g”, “#CC6600”, “b”, “r”]

List of vector colors to cycle through.

vector_widthint, default 5

Width of displayed vectors.

vector_stylestr, default ‘-|>’

Vector arrowhead style (from matplotlib’s arrow style).

vector_mutationint, default 20

viewlist, default [-60, 30]

Azimuthal and Elevation viewing angles.

xlabellist, default [“$x$”, “”]

List of strings corresponding to +x and -x axes labels, respectively.

xlposlist, default [1.1, -1.1]

Positions of +x and -x labels respectively.

ylabellist, default [“$y$”, “”]

List of strings corresponding to +y and -y axes labels, respectively.

ylposlist, default [1.2, -1.2]

Positions of +y and -y labels respectively.

zlabellist, default [‘$\left|0\right>$’, ‘$\left|1\right>$’]

List of strings corresponding to +z and -z axes labels, respectively.

zlposlist, default [1.2, -1.2]

Positions of +z and -z labels respectively.

add_annotation(state_or_vector, text, **kwargs)[source]

Add a text or LaTeX annotation to Bloch sphere, parametrized by a qubit state or a vector.

Parameters
state_or_vectorQobj/array/list/tuple

Position for the annotaion. Qobj of a qubit or a vector of 3 elements.

textstr

Annotation text. You can use LaTeX, but remember to use raw string e.g. r”$langle x rangle$” or escape backslashes e.g. “$\langle x \rangle$”.

kwargs :

Options as for mplot3d.axes3d.text, including: fontsize, color, horizontalalignment, verticalalignment.

add_points(points, meth='s')[source]

Add a list of data points to bloch sphere.

Parameters
pointsarray_like

Collection of data points.

meth{‘s’, ‘m’, ‘l’}

Type of points to plot, use ‘m’ for multicolored, ‘l’ for points connected with a line.

add_states(state, kind='vector')[source]

Add a state vector Qobj to Bloch sphere.

Parameters
stateQobj

Input state vector.

kind{‘vector’, ‘point’}

Type of object to plot.

add_vectors(vectors)[source]

Add a list of vectors to Bloch sphere.

Parameters
vectorsarray_like

Array with vectors of unit length or smaller.

clear()[source]

Resets Bloch sphere data sets to empty.

make_sphere()[source]

Plots Bloch sphere and data sets.

render()[source]

Render the Bloch sphere and its data sets in on given figure and axes.

save(name=None, format='png', dirc=None, dpin=None)[source]

Saves Bloch sphere to file of type format in directory dirc.

Parameters
namestr

Name of saved image. Must include path and format as well. i.e. ‘/Users/Paul/Desktop/bloch.png’ This overrides the ‘format’ and ‘dirc’ arguments.

formatstr

Format of output image.

dircstr

Directory for output images. Defaults to current working directory.

dpinint

Resolution in dots per inch.

Returns
File containing plot of Bloch sphere.
set_label_convention(convention)[source]

Set x, y and z labels according to one of conventions.

Parameters
conventionstring

One of the following:

show()[source]

Display Bloch sphere and corresponding data sets.

Notes

When using inline plotting in Jupyter notebooks, any figure created in a notebook cell is displayed after the cell executes. Thus if you create a figure yourself and use it create a Bloch sphere with b = Bloch(..., fig=fig) and then call b.show() in the same cell, then the figure will be displayed twice. If you do create your own figure, the simplest solution to this is to not call .show() in the cell you create the figure in.

vector_mutation

Sets the width of the vectors arrowhead

vector_style

Style of Bloch vectors, default = ‘-|>’ (or ‘simple’)

vector_width

Width of Bloch vectors, default = 5

## Distributions¶

class QFunc(xvec, yvec, g: float = 1.4142135623730951, memory: float = 1024)[source]

Class-based method of calculating the Husimi-Q function of many different quantum states at fixed phase-space points 0.5*g* (xvec + i*yvec). This class has slightly higher first-usage costs than qfunc, but subsequent operations will be several times faster. However, it can require quite a lot of memory. Call the created object as a function to retrieve the Husimi-Q function.

Parameters
xvec, yvecarray_like

x- and y-coordinates at which to calculate the Husimi-Q function.

gfloat, default sqrt(2)

Scaling factor for a = 0.5 * g * (x + iy). The value of g is related to the value of hbar in the commutation relation $$[x,\,y] = i\hbar$$ via $$\hbar=2/g^2$$, so the default corresponds to $$\hbar=1$$.

memoryreal, default 1024

Size in MB that may be used internally as workspace. This class will raise MemoryError if subsequently passed a state of sufficiently large dimension that this bound would be exceeded. In those cases, use qfunc with precompute_memory=None instead to force using the slower, more memory-efficient algorithm.

qfunc

a single function version, which will involve computing several quantities multiple times in order to use less memory.

Examples

Initialise the class for a square set of coordinates, with some states we want to investigate.

>>> xvec = np.linspace(-2, 2, 101)
>>> states = [qutip.rand_dm(10) for _ in [None]*10]
>>> qfunc = qutip.QFunc(xvec, xvec)


Now we can calculate the Husimi-Q function over each of the states more efficiently with:

>>> husimiq = np.array([qfunc(state) for state in states])


## Cubic Spline¶

class Cubic_Spline(a, b, y, alpha=0, beta=0)[source]

Calculates coefficients for a cubic spline interpolation of a given data set.

This function assumes that the data is sampled uniformly over a given interval.

Parameters
afloat

Lower bound of the interval.

bfloat

Upper bound of the interval.

yndarray

Function values at interval points.

alphafloat

Second-order derivative at a. Default is 0.

betafloat

Second-order derivative at b. Default is 0.

Notes

This object can be called like a normal function with a single or array of input points at which to evaluate the interplating function.

Habermann & Kindermann, “Multidimensional Spline Interpolation: Theory and Applications”, Comput Econ 30, 153 (2007).

Attributes
afloat

Lower bound of the interval.

bfloat

Upper bound of the interval.

coeffsndarray

Array of coeffcients defining cubic spline.

## Non-Markovian Solvers¶

class HEOMSolver[source]

This is superclass for all solvers that use the HEOM method for calculating the dynamics evolution. There are many references for this. A good introduction, and perhaps closest to the notation used here is: DOI:10.1103/PhysRevLett.104.250401 A more canonical reference, with full derivation is: DOI: 10.1103/PhysRevA.41.6676 The method can compute open system dynamics without using any Markovian or rotating wave approximation (RWA) for systems where the bath correlations can be approximated to a sum of complex eponentials. The method builds a matrix of linked differential equations, which are then solved used the same ODE solvers as other qutip solvers (e.g. mesolve)

This class should be treated as abstract. Currently the only subclass implemented is that for the Drude-Lorentz spectral density. This covers the majority of the work that has been done using this model, and there are some performance advantages to assuming this model where it is appropriate.

There are opportunities to develop a more general spectral density code.

Attributes
H_sysQobj

System Hamiltonian

coup_opQobj

Operator describing the coupling between system and bath.

coup_strengthfloat

Coupling strength.

temperaturefloat

Bath temperature, in units corresponding to planck

N_cutint

Cutoff parameter for the bath

N_expint

Number of exponential terms used to approximate the bath correlation functions

planckfloat

reduced Planck constant

boltzmannfloat

Boltzmann’s constant

optionsqutip.solver.Options

Generic solver options. If set to None the default options will be used

progress_bar: BaseProgressBar

Optional instance of BaseProgressBar, or a subclass thereof, for showing the progress of the simulation.

statsqutip.solver.Stats

optional container for holding performance statitics If None is set, then statistics are not collected There may be an overhead in collecting statistics

exp_coefflist of complex

Coefficients for the exponential series terms

exp_freqlist of complex

Frequencies for the exponential series terms

configure(H_sys, coup_op, coup_strength, temperature, N_cut, N_exp, planck=None, boltzmann=None, renorm=None, bnd_cut_approx=None, options=None, progress_bar=None, stats=None)[source]

Configure the solver using the passed parameters The parameters are described in the class attributes, unless there is some specific behaviour

Parameters
optionsqutip.solver.Options

Generic solver options. If set to None the default options will be used

progress_bar: BaseProgressBar

Optional instance of BaseProgressBar, or a subclass thereof, for showing the progress of the simulation. If set to None, then the default progress bar will be used Set to False for no progress bar

stats: :class:qutip.solver.Stats

Optional instance of solver.Stats, or a subclass thereof, for storing performance statistics for the solver If set to True, then the default Stats for this class will be used Set to False for no stats

create_new_stats()[source]

Creates a new stats object suitable for use with this solver Note: this solver expects the stats object to have sections

• config

• integrate

reset()[source]

Reset any attributes to default values

class HSolverDL(H_sys, coup_op, coup_strength, temperature, N_cut, N_exp, cut_freq, planck=1.0, boltzmann=1.0, renorm=True, bnd_cut_approx=True, options=None, progress_bar=None, stats=None)[source]

HEOM solver based on the Drude-Lorentz model for spectral density. Drude-Lorentz bath the correlation functions can be exactly analytically expressed as an infinite sum of exponentials which depend on the temperature, these are called the Matsubara terms or Matsubara frequencies

For practical computation purposes an approximation must be used based on a small number of Matsubara terms (typically < 4).

Attributes
cut_freqfloat

Bath spectral density cutoff frequency.

renormbool

Apply renormalisation to coupling terms Can be useful if using SI units for planck and boltzmann

bnd_cut_approxbool

Use boundary cut off approximation Can be

configure(H_sys, coup_op, coup_strength, temperature, N_cut, N_exp, cut_freq, planck=None, boltzmann=None, renorm=None, bnd_cut_approx=None, options=None, progress_bar=None, stats=None)[source]

Calls configure from HEOMSolver and sets any attributes that are specific to this subclass

reset()[source]

Reset any attributes to default values

run(rho0, tlist)[source]

Function to solve for an open quantum system using the HEOM model.

Parameters
rho0Qobj

Initial state (density matrix) of the system.

tlistlist

Time over which system evolves.

Returns
resultsqutip.solver.Result

Object storing all results from the simulation.

class MemoryCascade(H_S, L1, L2, S_matrix=None, c_ops_markov=None, integrator='propagator', parallel=False, options=None)[source]

Class for running memory cascade simulations of open quantum systems with time-delayed coherent feedback.

Attributes
H_Squtip.Qobj

System Hamiltonian (can also be a Liouvillian)

L1

System operators coupling into the feedback loop. Can be a single operator or a list of operators.

L2

System operators coupling out of the feedback loop. Can be a single operator or a list of operators. L2 must have the same length as L1.

S_matrix: *array*

S matrix describing which operators in L1 are coupled to which operators in L2 by the feedback channel. Defaults to an n by n identity matrix where n is the number of elements in L1/L2.

c_ops_markov

Decay operators describing conventional Markovian decay channels. Can be a single operator or a list of operators.

integratorstr {‘propagator’, ‘mesolve’}

Integrator method to use. Defaults to ‘propagator’ which tends to be faster for long times (i.e., large Hilbert space).

parallelbool

Run integrator in parallel if True. Only implemented for ‘propagator’ as the integrator method.

optionsqutip.solver.Options

Generic solver options.

outfieldcorr(rho0, blist, tlist, tau, c1=None, c2=None)[source]

Compute output field expectation value <O_n(tn)…O_2(t2)O_1(t1)> for times t1,t2,… and O_i = I, b_out, b_out^dagger, b_loop, b_loop^dagger

Parameters
rho0qutip.Qobj

initial density matrix or state vector (ket).

blistarray_like

List of integers specifying the field operators: 0: I (nothing) 1: b_out 2: b_out^dagger 3: b_loop 4: b_loop^dagger

tlistarray_like

list of corresponding times t1,..,tn at which to evaluate the field operators

taufloat

time-delay

c1qutip.Qobj

system collapse operator that couples to the in-loop field in question (only needs to be specified if self.L1 has more than one element)

c2qutip.Qobj

system collapse operator that couples to the output field in question (only needs to be specified if self.L2 has more than one element)

Returns
: complex

expectation value of field correlation function

outfieldpropagator(blist, tlist, tau, c1=None, c2=None, notrace=False)[source]

Compute propagator for computing output field expectation values <O_n(tn)…O_2(t2)O_1(t1)> for times t1,t2,… and O_i = I, b_out, b_out^dagger, b_loop, b_loop^dagger

Parameters
blistarray_like

List of integers specifying the field operators: 0: I (nothing) 1: b_out 2: b_out^dagger 3: b_loop 4: b_loop^dagger

tlistarray_like

list of corresponding times t1,..,tn at which to evaluate the field operators

taufloat

time-delay

c1qutip.Qobj

system collapse operator that couples to the in-loop field in question (only needs to be specified if self.L1 has more than one element)

c2qutip.Qobj

system collapse operator that couples to the output field in question (only needs to be specified if self.L2 has more than one element)

notracebool {False}

If this optional is set to True, a propagator is returned for a cascade of k systems, where $$(k-1) tau < t < k tau$$. If set to False (default), a generalized partial trace is performed and a propagator for a single system is returned.

Returns
: qutip.Qobj

time-propagator for computing field correlation function

propagator(t, tau, notrace=False)[source]

Compute propagator for time t and time-delay tau

Parameters
tfloat

current time

taufloat

time-delay

notracebool {False}

If this optional is set to True, a propagator is returned for a cascade of k systems, where $$(k-1) tau < t < k tau$$. If set to False (default), a generalized partial trace is performed and a propagator for a single system is returned.

Returns
——-
: :class:qutip.Qobj

time-propagator for reduced system dynamics

rhot(rho0, t, tau)[source]

Compute the reduced system density matrix $$\rho(t)$$

Parameters
rho0qutip.Qobj

initial density matrix or state vector (ket)

tfloat

current time

taufloat

time-delay

Returns
: qutip.Qobj

density matrix at time $$t$$

class TTMSolverOptions(dynmaps=None, times=[], learningtimes=[], thres=0.0, options=None)[source]

Class of options for the Transfer Tensor Method solver.

Attributes
dynmapslist of qutip.Qobj

List of precomputed dynamical maps (superoperators), or a callback function that returns the superoperator at a given time.

timesarray_like

List of times $$t_n$$ at which to calculate $$\rho(t_n)$$

learningtimesarray_like

List of times $$t_k$$ to use as learning times if argument dynmaps is a callback function.

thresfloat

Threshold for halting. Halts if $$||T_{n}-T_{n-1}||$$ is below treshold.

optionsqutip.solver.Options

Generic solver options.

## Solver Options and Results¶

class ExpectOps(e_ops=[], super_=False)[source]

Contain and compute expectation values

class Options(atol=1e-08, rtol=1e-06, method='adams', order=12, nsteps=1000, first_step=0, max_step=0, min_step=0, average_expect=True, average_states=False, tidy=True, num_cpus=0, norm_tol=0.001, norm_t_tol=1e-06, norm_steps=5, rhs_reuse=False, rhs_filename=None, ntraj=500, gui=False, rhs_with_state=False, store_final_state=False, store_states=False, steady_state_average=False, seeds=None, normalize_output=True, use_openmp=None, openmp_threads=None)[source]

Class of options for evolution solvers such as qutip.mesolve and qutip.mcsolve. Options can be specified either as arguments to the constructor:

opts = Options(order=10, ...)


or by changing the class attributes after creation:

opts = Options()
opts.order = 10


Returns options class to be used as options in evolution solvers.

Attributes
atolfloat {1e-8}

Absolute tolerance.

rtolfloat {1e-6}

Relative tolerance.

Integration method.

orderint {12}

Order of integrator (<=12 ‘adams’, <=5 ‘bdf’)

nstepsint {2500}

Max. number of internal steps/call.

first_stepfloat {0}

Size of initial step (0 = automatic).

min_stepfloat {0}

Minimum step size (0 = automatic).

max_stepfloat {0}

Maximum step size (0 = automatic)

tidybool {True,False}

Tidyup Hamiltonian and initial state by removing small terms.

num_cpusint

Number of cpus used by mcsolver (default = # of cpus).

norm_tolfloat

Tolerance used when finding wavefunction norm in mcsolve.

norm_stepsint

Max. number of steps used to find wavefunction norm to within norm_tol in mcsolve.

average_statesbool {False}

Average states values over trajectories in stochastic solvers.

average_expectbool {True}

Average expectation values over trajectories for stochastic solvers.

mc_corr_epsfloat {1e-10}

Arbitrarily small value for eliminating any divide-by-zero errors in correlation calculations when using mcsolve.

ntrajint {500}

Number of trajectories in stochastic solvers.

Number of OPENMP threads to use. Default is number of cpu cores.

rhs_reusebool {False,True}

Reuse Hamiltonian data.

rhs_with_statebool {False,True}

Whether or not to include the state in the Hamiltonian function callback signature.

rhs_filenamestr

Name for compiled Cython file.

seedsndarray

Array containing random number seeds for mcsolver.

store_final_statebool {False, True}

Whether or not to store the final state of the evolution in the result class.

store_statesbool {False, True}

Whether or not to store the state vectors or density matrices in the result class, even if expectation values operators are given. If no expectation are provided, then states are stored by default and this option has no effect.

use_openmpbool {True, False}

Use OPENMP for sparse matrix vector multiplication. Default None means auto check.

class Result[source]

Class for storing simulation results from any of the dynamics solvers.

Attributes
solverstr

Which solver was used [e.g., ‘mesolve’, ‘mcsolve’, ‘brmesolve’, …]

timeslist/array

Times at which simulation data was collected.

expectlist/array

Expectation values (if requested) for simulation.

statesarray

State of the simulation (density matrix or ket) evaluated at times.

num_expectint

Number of expectation value operators in simulation.

num_collapseint

Number of collapse operators in simualation.

ntrajint/list

Number of trajectories (for stochastic solvers). A list indicates that averaging of expectation values was done over a subset of total number of trajectories.

col_timeslist

Times at which state collpase occurred. Only for Monte Carlo solver.

col_whichlist

Which collapse operator was responsible for each collapse in col_times. Only for Monte Carlo solver.

class SolverConfiguration[source]
class Stats(section_names=None)[source]

Statistical information on the solver performance Statistics can be grouped into sections. If no section names are given in the the contructor, then all statistics will be added to one section ‘main’

Parameters
section_nameslist

list of keys that will be used as keys for the sections These keys will also be used as names for the sections The text in the output can be overidden by setting the header property of the section If no names are given then one section called ‘main’ is created

Attributes
sectionsOrderedDict of _StatsSection

These are the sections that are created automatically on instantiation or added using add_section

Some text that will be used as the heading in the report By default there is None

total_timefloat

Time in seconds for the solver to complete processing Can be None, meaning that total timing percentages will be reported

add_count(key, value, section=None)[source]

Add value to count. If key does not already exist in section then it is created with this value. If key already exists it is increased by the give value value is expected to be an integer

Parameters
keystring

key for the section.counts dictionary reusing a key will result in numerical addition of value

valueint

Initial value of the count, or added to an existing count

sectionstring or _StatsSection

Section which to add the count to. If None given, the default (first) section will be used

add_message(key, value, section=None, sep=';')[source]

Add value to message. If key does not already exist in section then it is created with this value. If key already exists the value is added to the message The value will be converted to a string

Parameters
keystring

key for the section.messages dictionary reusing a key will result in concatenation of value

valueint

Initial value of the message, or added to an existing message

sepstring

Message will be prefixed with this string when concatenating

section: string or class_StatsSection

Section which to add the message to. If None given, the default (first) section will be used

add_section(name)[source]

Add another section with the given name

Parameters
namestring

will be used as key for sections dict will also be the header for the section

Returns
section_StatsSection

The new section

add_timing(key, value, section=None)[source]

Add value to timing. If key does not already exist in section then it is created with this value. If key already exists it is increased by the give value value is expected to be a float, and given in seconds.

Parameters
keystring

key for the section.timings dictionary reusing a key will result in numerical addition of value

valueint

Initial value of the timing, or added to an existing timing

section: string or class_StatsSection

Section which to add the timing to. If None given, the default (first) section will be used

clear()[source]

Clear counts, timings and messages from all sections

report(output=<_io.TextIOWrapper name='<stdout>' mode='w' encoding='utf-8'>)[source]

Report the counts, timings and messages from the sections. Sections are reported in the order that the names were supplied in the constructor. The counts, timings and messages are reported in the order that they are added to the sections The output can be written to anything that supports a write method, e.g. a file or the console (default) The output is intended to in markdown format

Parameters
outputstream

file or console stream - anything that support write - where the output will be written

set_total_time(value, section=None)[source]

Sets the total time for the complete solve or for a specific section value is expected to be a float, and given in seconds

Parameters
valuefloat

Time in seconds to complete the solver section

sectionstring or class

Section which to set the total_time for If None given, the total_time for complete solve is set

class StochasticSolverOptions(me, H=None, c_ops=[], sc_ops=[], state0=None, e_ops=[], m_ops=None, store_all_expect=False, store_measurement=False, dW_factors=None, solver=None, method='homodyne', normalize=None, times=None, nsubsteps=1, ntraj=1, tol=None, generate_noise=None, noise=None, progress_bar=None, map_func=None, map_kwargs=None, args={}, options=None, noiseDepth=20)[source]

Class of options for stochastic solvers such as qutip.stochastic.ssesolve, qutip.stochastic.smesolve, etc.

The stochastic solvers qutip.stochastic.general_stochastic, qutip.stochastic.ssesolve, qutip.stochastic.smesolve, qutip.stochastic.photocurrent_sesolve and qutip.stochastic.photocurrent_mesolve all take the same keyword arguments as the constructor of these class, and internally they use these arguments to construct an instance of this class, so it is rarely needed to explicitly create an instance of this class.

Within the attribute list, a time_dependent_object is either

• Qobj: a constant term

• 2-element list of [Qobj, time_dependence]: a time-dependent term where the Qobj will be multiplied by the time-dependent scalar.

For more details on all allowed time-dependent objects, see the documentation for QobjEvo.

Attributes
Htime_dependent_object or list of time_dependent_object

System Hamiltonian in standard time-dependent list format. This is the same as the argument that (e.g.) mesolve takes. If this is a list of elements, they are summed.

state0qutip.Qobj

Initial state vector (ket) or density matrix.

timesarray_like of float

List of times for $$t$$. Must be uniformly spaced.

c_opslist of time_dependent_object

List of deterministic collapse operators. Each element of the list is a separate operator; unlike the Hamiltonian, there is no implicit summation over the terms.

sc_opslist of time_dependent_object

List of stochastic collapse operators. Each stochastic collapse operator will give a deterministic and stochastic contribution to the equation of motion according to how the d1 and d2 functions are defined. Each element of the list is a separate operator, like c_ops.

e_opslist of qutip.Qobj

Single operator or list of operators for which to evaluate expectation values.

m_opslist of qutip.Qobj

List of operators representing the measurement operators. The expected format is a nested list with one measurement operator for each stochastic increament, for each stochastic collapse operator.

argsdict

Dictionary of parameters for time dependent systems.

tolfloat

Tolerance of the solver for implicit methods.

ntrajint

Number of trajectors.

nsubstepsint

Number of sub steps between each time-spep given in times.

dW_factorsarray

Array of length len(sc_ops), containing scaling factors for each measurement operator in m_ops.

solverstring

Name of the solver method to use for solving the stochastic equations. Valid values are:

• order 1/2 algorithms: ‘euler-maruyama’, ‘pc-euler’, ‘pc-euler-imp’

• order 1 algorithms: ‘milstein’, ‘platen’, ‘milstein-imp’, ‘rouchon’

• order 3/2 algorithms: ‘taylor1.5’, ‘taylor1.5-imp’, ‘explicit1.5’

• order 2 algorithms: ‘taylor2.0’

See the documentation of stochastic_solvers for a description of the solvers. Implicit methods can adjust tolerance via the kw ‘tol’. Default is {‘tol’: 1e-6}

methodstring (‘homodyne’, ‘heterodyne’)

The name of the type of measurement process that give rise to the stochastic equation to solve.

store_all_expectbool (default False)

Whether or not to store the e_ops expect values for all paths.

store_measurementbool (default False)

Whether or not to store the measurement results in the qutip.solver.Result instance returned by the solver.

noiseint, or 1D array of int, or 4D array of float
• int : seed of the noise

• 1D array : length = ntraj, seeds for each trajectories.

• 4D array : (ntraj, len(times), nsubsteps, len(sc_ops)*[1|2]). Vector for the noise, the len of the last dimensions is doubled for solvers of order 1.5. This corresponds to results.noise.

noiseDepthint

Number of terms kept of the truncated series used to create the noise used by taylor2.0 solver.

normalizebool

(default True for (photo)ssesolve, False for (photo)smesolve) Whether or not to normalize the wave function during the evolution. Normalizing density matrices introduce numerical errors.

optionsqutip.solver.Options

Generic solver options. Only options.average_states and options.store_states are used.

map_func: function

A map function or managing the calls to single-trajactory solvers.

map_kwargs: dictionary

Optional keyword arguments to the map_func function function.

progress_barqutip.ui.BaseProgressBar

Optional progress bar class instance.

## Permutational Invariance¶

class Dicke(N, hamiltonian=None, emission=0.0, dephasing=0.0, pumping=0.0, collective_emission=0.0, collective_dephasing=0.0, collective_pumping=0.0)[source]

The Dicke class which builds the Lindbladian and Liouvillian matrix.

Parameters
N: int

The number of two-level systems.

hamiltonianqutip.Qobj

A Hamiltonian in the Dicke basis.

The matrix dimensions are (nds, nds), with nds being the number of Dicke states. The Hamiltonian can be built with the operators given by the jspin functions.

emission: float

Incoherent emission coefficient (also nonradiative emission). default: 0.0

dephasing: float

Local dephasing coefficient. default: 0.0

pumping: float

Incoherent pumping coefficient. default: 0.0

collective_emission: float

Collective (superradiant) emmission coefficient. default: 0.0

collective_pumping: float

Collective pumping coefficient. default: 0.0

collective_dephasing: float

Collective dephasing coefficient. default: 0.0

Examples

>>> from piqs import Dicke, jspin
>>> N = 2
>>> jx, jy, jz = jspin(N)
>>> jp = jspin(N, "+")
>>> jm = jspin(N, "-")
>>> ensemble = Dicke(N, emission=1.)
>>> L = ensemble.liouvillian()

Attributes
N: int

The number of two-level systems.

hamiltonianqutip.Qobj

A Hamiltonian in the Dicke basis.

The matrix dimensions are (nds, nds), with nds being the number of Dicke states. The Hamiltonian can be built with the operators given by the jspin function in the “dicke” basis.

emission: float

Incoherent emission coefficient (also nonradiative emission). default: 0.0

dephasing: float

Local dephasing coefficient. default: 0.0

pumping: float

Incoherent pumping coefficient. default: 0.0

collective_emission: float

Collective (superradiant) emmission coefficient. default: 0.0

collective_dephasing: float

Collective dephasing coefficient. default: 0.0

collective_pumping: float

Collective pumping coefficient. default: 0.0

nds: int

The number of Dicke states.

dshape: tuple

The shape of the Hilbert space in the Dicke or uncoupled basis. default: (nds, nds).

c_ops()[source]

Build collapse operators in the full Hilbert space 2^N.

Returns
c_ops_list: list

The list with the collapse operators in the 2^N Hilbert space.

coefficient_matrix()[source]

Build coefficient matrix for ODE for a diagonal problem.

Returns
M: ndarray

The matrix M of the coefficients for the ODE dp/dt = Mp. p is the vector of the diagonal matrix elements of the density matrix rho in the Dicke basis.

lindbladian()[source]

Build the Lindbladian superoperator of the dissipative dynamics.

Returns
lindbladianqutip.Qobj

The Lindbladian matrix as a qutip.Qobj.

liouvillian()[source]

Build the total Liouvillian using the Dicke basis.

Returns
liouvqutip.Qobj

The Liouvillian matrix for the system.

pisolve(initial_state, tlist, options=None)[source]

Solve for diagonal Hamiltonians and initial states faster.

Parameters
initial_statequtip.Qobj

An initial state specified as a density matrix of qutip.Qbj type.

tlist: ndarray

A 1D numpy array of list of timesteps to integrate

optionsqutip.solver.Options

The options for the solver.

Returns
result: list

A dictionary of the type qutip.solver.Result which holds the results of the evolution.

class Pim(N, emission=0.0, dephasing=0, pumping=0, collective_emission=0, collective_pumping=0, collective_dephasing=0)[source]

The Permutation Invariant Matrix class.

Initialize the class with the parameters for generating a Permutation Invariant matrix which evolves a given diagonal initial state p as:

dp/dt = Mp

Parameters
N: int

The number of two-level systems.

emission: float

Incoherent emission coefficient (also nonradiative emission). default: 0.0

dephasing: float

Local dephasing coefficient. default: 0.0

pumping: float

Incoherent pumping coefficient. default: 0.0

collective_emission: float

Collective (superradiant) emmission coefficient. default: 0.0

collective_pumping: float

Collective pumping coefficient. default: 0.0

collective_dephasing: float

Collective dephasing coefficient. default: 0.0

Attributes
N: int

The number of two-level systems.

emission: float

Incoherent emission coefficient (also nonradiative emission). default: 0.0

dephasing: float

Local dephasing coefficient. default: 0.0

pumping: float

Incoherent pumping coefficient. default: 0.0

collective_emission: float

Collective (superradiant) emmission coefficient. default: 0.0

collective_dephasing: float

Collective dephasing coefficient. default: 0.0

collective_pumping: float

Collective pumping coefficient. default: 0.0

M: dict

A nested dictionary of the structure {row: {col: val}} which holds non zero elements of the matrix M

calculate_j_m(dicke_row, dicke_col)[source]

Get the value of j and m for the particular Dicke space element.

Parameters
dicke_row, dicke_col: int

The row and column from the Dicke space matrix

Returns
j, m: float

The j and m values.

calculate_k(dicke_row, dicke_col)[source]

Get k value from the current row and column element in the Dicke space.

Parameters
dicke_row, dicke_col: int

The row and column from the Dicke space matrix.

Returns
——-
k: int

The row index for the matrix M for given Dicke space element.

coefficient_matrix()[source]

Generate the matrix M governing the dynamics for diagonal cases.

If the initial density matrix and the Hamiltonian is diagonal, the evolution of the system is given by the simple ODE: dp/dt = Mp.

isdicke(dicke_row, dicke_col)[source]

Check if an element in a matrix is a valid element in the Dicke space. Dicke row: j value index. Dicke column: m value index. The function returns True if the element exists in the Dicke space and False otherwise.

Parameters
dicke_row, dicke_colint

Index of the element in Dicke space which needs to be checked

solve(rho0, tlist, options=None)[source]

Solve the ODE for the evolution of diagonal states and Hamiltonians.

tau1(j, m)[source]

Calculate coefficient matrix element relative to (j, m, m).

tau2(j, m)[source]

Calculate coefficient matrix element relative to (j, m+1, m+1).

tau3(j, m)[source]

Calculate coefficient matrix element relative to (j+1, m+1, m+1).

tau4(j, m)[source]

Calculate coefficient matrix element relative to (j-1, m+1, m+1).

tau5(j, m)[source]

Calculate coefficient matrix element relative to (j+1, m, m).

tau6(j, m)[source]

Calculate coefficient matrix element relative to (j-1, m, m).

tau7(j, m)[source]

Calculate coefficient matrix element relative to (j+1, m-1, m-1).

tau8(j, m)[source]

Calculate coefficient matrix element relative to (j, m-1, m-1).

tau9(j, m)[source]

Calculate coefficient matrix element relative to (j-1, m-1, m-1).

tau_valid(dicke_row, dicke_col)[source]

Find the Tau functions which are valid for this value of (dicke_row, dicke_col) given the number of TLS. This calculates the valid tau values and reurns a dictionary specifying the tau function name and the value.

Parameters
dicke_row, dicke_colint

Index of the element in Dicke space which needs to be checked.

Returns
taus: dict

A dictionary of key, val as {tau: value} consisting of the valid taus for this row and column of the Dicke space element.

## One-Dimensional Lattice¶

class Lattice1d(num_cell=10, boundary='periodic', cell_num_site=1, cell_site_dof=[1], Hamiltonian_of_cell=None, inter_hop=None)[source]

A class for representing a 1d crystal.

The Lattice1d class can be defined with any specific unit cells and a specified number of unit cells in the crystal. It can return dispersion relationship, position operators, Hamiltonian in the position represention etc.

Parameters
num_cellint

The number of cells in the crystal.

boundarystr

Specification of the type of boundary the crystal is defined with.

cell_num_siteint

The number of sites in the unit cell.

cell_site_doflist of int/ int

The tensor structure of the degrees of freedom at each site of a unit cell.

Hamiltonian_of_cellqutip.Qobj

The Hamiltonian of the unit cell.

inter_hopqutip.Qobj / list of Qobj

The coupling between the unit cell at i and at (i+unit vector)

Attributes
num_cellint

The number of unit cells in the crystal.

cell_num_siteint

The nuber of sites in a unit cell.

length_for_siteint

The length of the dimension per site of a unit cell.

cell_tensor_configlist of int

The tensor structure of the cell in the form [cell_num_site,cell_site_dof[:][0] ]

lattice_tensor_configlist of int

The tensor structure of the crystal in the form [num_cell,cell_num_site,cell_site_dof[:][0]]

length_of_unit_cellint

The length of the dimension for a unit cell.

period_bnd_cond_xint

1 indicates “periodic” and 0 indicates “hardwall” boundary condition

inter_vec_listlist of list

The list of list of coefficients of inter unitcell vectors’ components along Cartesian uit vectors.

lattice_vectors_listlist of list

The list of list of coefficients of lattice basis vectors’ components along Cartesian unit vectors.

H_intraqutip.Qobj

The Qobj storing the Hamiltonian of the unnit cell.

H_inter_listlist of Qobj/ qutip.Qobj

The list of coupling terms between unit cells of the lattice.

is_realbool

Indicates if the Hamiltonian is real or not.

Hamiltonian()[source]

Returns the lattice Hamiltonian for the instance of Lattice1d.

Returns
Qobj(Hamil)qutip.Qobj

oper type Quantum object representing the lattice Hamiltonian.

basis(cell, site, dof_ind)[source]

Returns a single particle wavefunction ket with the particle localized at a specified dof at a specified site of a specified cell.

Parameters
• cell (int) – The cell at which the particle is to be localized.

• site (int) – The site of the cell at which the particle is to be localized.

• dof_ind (int/ list of int) – The index of the degrees of freedom with which the sigle particle is to be localized.

Returns
vec_iqutip.Qobj

ket type Quantum object representing the localized particle.

bloch_wave_functions()[source]

Returns eigenvectors ($psi_n(k)$) of the Hamiltonian in a numpy.ndarray for translationally symmetric lattices with periodic boundary condition.

\begin{eqnarray} |\psi_n(k) \rangle = |k \rangle \otimes | u_{n}(k) \rangle \\ | u_{n}(k) \rangle = a_n(k)|a\rangle + b_n(k)|b\rangle \\ \end{eqnarray}

Please see section 1.2 of Asbóth, J. K., Oroszlány, L., & Pályi, A. (2016). A short course on topological insulators. Lecture notes in physics, 919 for a review.

Returns
eigenstatesordered np.array

eigenstates[j][0] is the jth eigenvalue. eigenstates[j][1] is the corresponding eigenvector.

bulk_Hamiltonians()[source]

Returns the bulk momentum space Hamiltonian ($H(k)$) for the lattice at the good quantum numbers of k in a numpy ndarray of Qobj’s.

Please see section 1.2 of Asbóth, J. K., Oroszlány, L., & Pályi, A. (2016). A short course on topological insulators. Lecture notes in physics, 919 for a review.

Returns
knxanp.array

knxA[j][0] is the jth good Quantum number k.

qH_ksnp.ndarray of Qobj’s

qH_ks[j] is the Oobj of type oper that holds a bulk Hamiltonian for a good quantum number k.

cell_periodic_parts()[source]

Returns eigenvectors of the bulk Hamiltonian, i.e. the cell periodic part($u_n(k)$) of the Bloch wavefunctios in a numpy.ndarray for translationally symmetric lattices with periodic boundary condition.

\begin{eqnarray} |\psi_n(k) \rangle = |k \rangle \otimes | u_{n}(k) \rangle \\ | u_{n}(k) \rangle = a_n(k)|a\rangle + b_n(k)|b\rangle \\ \end{eqnarray}

Please see section 1.2 of Asbóth, J. K., Oroszlány, L., & Pályi, A. (2016). A short course on topological insulators. Lecture notes in physics, 919 for a review.

Returns
knxanp.array

knxA[j][0] is the jth good Quantum number k.

vec_knsnp.ndarray of Qobj’s

vec_kns[j] is the Oobj of type ket that holds an eigenvector of the bulk Hamiltonian of the lattice.

display_lattice()[source]

Produces a graphic portraying the lattice symbolically with a unit cell marked in it.

Returns
inter_TQobj

The coefficient of $psi_{i,N}^{dagger}psi_{0,i+1}$, i.e. the coupling between the two boundary sites of the two unit cells i and i+1.

display_unit_cell(label_on=False)[source]

Produces a graphic displaying the unit cell features with labels on if defined by user. Also returns a dict of Qobj’s corresponding to the labeled elements on the display.

Returns
Hcelldict

Hcell[i][j] is the Hamiltonian segment for $H_{i,j}$ labeled on the graphic.

distribute_operator(op)[source]

A function that returns an operator matrix that applies op to all the cells in the 1d lattice

Parameters

op (qutip.Qobj) – Qobj representing the operator to be applied at all cells.

Returns
op_Hqutip.Qobj

Quantum object representing the operator with op applied at all cells.

get_dispersion(knpoints=0)[source]

Returns dispersion relationship for the lattice with the specified number of unit cells with a k array and a band energy array.

Returns
knxanp.array

knxA[j][0] is the jth good Quantum number k.

val_knsnp.array

val_kns[j][:] is the array of band energies of the jth band good at all the good Quantum numbers of k.

k()[source]

Returns the crystal momentum operator. All degrees of freedom has the cell number at their correspondig entry in the position operator.

Returns
Qobj(ks)qutip.Qobj

The crystal momentum operator in units of 1/a. L is the number of unit cells, a is the length of a unit cell which is always taken to be 1.

operator_at_cells(op, cells)[source]

A function that returns an operator matrix that applies op to specific cells specified in the cells list

Parameters
opqutip.Qobj

Qobj representing the operator to be applied at certain cells.

cells: list of int

The cells at which the operator op is to be applied.

Returns
Qobj(op_H)Qobj

Quantum object representing the operator with op applied at the specified cells.

operator_between_cells(op, row_cell, col_cell)[source]

A function that returns an operator matrix that applies op to specific cells specified in the cells list

Parameters
opqutip.Qobj

Qobj representing the operator to be put between cells row_cell and col_cell.

row_cell: int

The row index for cell for the operator op to be applied.

col_cell: int

The column index for cell for the operator op to be applied.

Returns
oper_bet_cellQobj

Quantum object representing the operator with op applied between the specified cells.

plot_dispersion()[source]

Plots the dispersion relationship for the lattice with the specified number of unit cells. The dispersion of the infinte crystal is also plotted if num_cell is smaller than MAXc.

winding_number()[source]

Returns the winding number for a lattice that has chiral symmetry and also plots the trajectory of (dx,dy)(dx,dy are the coefficients of sigmax and sigmay in the Hamiltonian respectively) on a plane.

Returns
winding_numberint or str

knxA[j][0] is the jth good Quantum number k.

x()[source]

Returns the position operator. All degrees of freedom has the cell number at their correspondig entry in the position operator.

Returns
Qobj(xs)qutip.Qobj

The position operator.

## Distribution functions¶

class Distribution(data=None, xvecs=[], xlabels=[])[source]

A class for representation spatial distribution functions.

The Distribution class can be used to prepresent spatial distribution functions of arbitray dimension (although only 1D and 2D distributions are used so far).

It is indented as a base class for specific distribution function, and provide implementation of basic functions that are shared among all Distribution functions, such as visualization, calculating marginal distributions, etc.

Parameters
dataarray_like

Data for the distribution. The dimensions must match the lengths of the coordinate arrays in xvecs.

xvecslist

List of arrays that spans the space for each coordinate.

xlabelslist

List of labels for each coordinate.

marginal(dim=0)[source]

Calculate the marginal distribution function along the dimension dim. Return a new Distribution instance describing this reduced- dimensionality distribution.

Parameters
dimint

The dimension (coordinate index) along which to obtain the marginal distribution.

Returns
dDistributions

A new instances of Distribution that describes the marginal distribution.

project(dim=0)[source]

Calculate the projection (max value) distribution function along the dimension dim. Return a new Distribution instance describing this reduced-dimensionality distribution.

Parameters
dimint

The dimension (coordinate index) along which to obtain the projected distribution.

Returns
dDistributions

A new instances of Distribution that describes the projection.

visualize(fig=None, ax=None, figsize=(8, 6), colorbar=True, cmap=None, style='colormap', show_xlabel=True, show_ylabel=True)[source]

Visualize the data of the distribution in 1D or 2D, depending on the dimensionality of the underlaying distribution.

Parameters:

figmatplotlib Figure instance

If given, use this figure instance for the visualization,

axmatplotlib Axes instance

If given, render the visualization using this axis instance.

figsizetuple

Size of the new Figure instance, if one needs to be created.

colorbar: Bool

Whether or not the colorbar (in 2D visualization) should be used.

cmap: matplotlib colormap instance

If given, use this colormap for 2D visualizations.

stylestring

Type of visualization: ‘colormap’ (default) or ‘surface’.

Returns
fig, axtuple

A tuple of matplotlib figure and axes instances.

class WignerDistribution(rho=None, extent=[[- 5, 5], [- 5, 5]], steps=250)[source]
class QDistribution(rho=None, extent=[[- 5, 5], [- 5, 5]], steps=250)[source]
class TwoModeQuadratureCorrelation(state=None, theta1=0.0, theta2=0.0, extent=[[- 5, 5], [- 5, 5]], steps=250)[source]
update(state)[source]

calculate probability distribution for quadrature measurement outcomes given a two-mode wavefunction or density matrix

update_psi(psi)[source]

calculate probability distribution for quadrature measurement outcomes given a two-mode wavefunction

update_rho(rho)[source]

calculate probability distribution for quadrature measurement outcomes given a two-mode density matrix

class HarmonicOscillatorWaveFunction(psi=None, omega=1.0, extent=[- 5, 5], steps=250)[source]
update(psi)[source]

Calculate the wavefunction for the given state of an harmonic oscillator

class HarmonicOscillatorProbabilityFunction(rho=None, omega=1.0, extent=[- 5, 5], steps=250)[source]
update(rho)[source]

Calculate the probability function for the given state of an harmonic oscillator (as density matrix)

## Quantum information processing¶

class Gate(*args, **kwargs)[source]

Representation of a quantum gate, with its required parametrs, and target and control qubits.

Parameters
namestring

Gate name.

targetslist or int

Gate targets.

controlslist or int

Gate controls.

arg_valuefloat

Argument value(phi).

arg_labelstring

Label for gate representation.

classical_controlsint or list of int, optional

indices of classical bits to control gate on.

control_valueint, optional

value of classical bits to control on, the classical controls are interpreted as an integer with lowest bit being the first one. If not specified, then the value is interpreted to be 2 ** len(classical_controls) - 1 (i.e. all classical controls are 1).

class Measurement(name, targets=None, index=None, classical_store=None)[source]

Representation of a quantum measurement, with its required parameters, and target qubits.

Parameters
namestring

Measurement name.

targetslist or int

Gate targets.

classical_storeint

Result of the measurment is stored in this classical register of the circuit.

measurement_comp_basis(state)[source]

Measures a particular qubit (determined by the target) whose ket vector/ density matrix is specified in the computational basis and returns collapsed_states and probabilities (retains full dimension).

Parameters
stateket or oper

state to be measured on specified by ket vector or density matrix

Returns
collapsed_statesList of Qobjs

the collapsed state obtained after measuring the qubits and obtaining the qubit specified by the target in the state specified by the index.

probabilitiesList of floats

the probability of measuring a state in a the state specified by the index.

class QubitCircuit(N, input_states=None, output_states=None, reverse_states=True, user_gates=None, dims=None, num_cbits=0)[source]

Representation of a quantum program/algorithm, maintaining a sequence of gates.

Parameters
Nint

Number of qubits in the system.

user_gatesdict

Define a dictionary of the custom gates. See examples for detail.

input_stateslist

A list of string such as 0,’+’, “A”, “Y”. Only used for latex.

dimslist

A list of integer for the dimension of each composite system. e.g [2,2,2,2,2] for 5 qubits system. If None, qubits system will be the default option.

num_cbitsint

Number of classical bits in the system.

Examples

>>> def user_gate():
...     mat = np.array([[1.,   0],
...                     [0., 1.j]])
...     return Qobj(mat, dims=[[2], [2]])
>>> qubit_circuit = QubitCircuit(2, user_gates={"T":user_gate})

add_1q_gate(name, start=0, end=None, qubits=None, arg_value=None, arg_label=None, classical_controls=None, control_value=None)[source]

Adds a single qubit gate with specified parameters on a variable number of qubits in the circuit. By default, it applies the given gate to all the qubits in the register.

Parameters
namestring

Gate name.

startint

Starting location of qubits.

endint

Last qubit for the gate.

qubitslist

Specific qubits for applying gates.

arg_valuefloat

Argument value(phi).

arg_labelstring

Label for gate representation.

add_circuit(qc, start=0)[source]

Adds a block of a qubit circuit to the main circuit. Globalphase gates are not added.

Parameters
qcQubitCircuit

The circuit block to be added to the main circuit.

startint

The qubit on which the first gate is applied.

add_gate(gate, targets=None, controls=None, arg_value=None, arg_label=None, index=None, classical_controls=None, control_value=None)[source]

Adds a gate with specified parameters to the circuit.

Parameters
gate: string or :class:.Gate

Gate name. If gate is an instance of Gate, parameters are unpacked and added.

targets: list

Gate targets.

controls: list

Gate controls.

arg_value: float

Argument value(phi).

arg_label: string

Label for gate representation.

indexlist

classical_controlsint or list of int, optional

indices of classical bits to control gate on.

control_valueint, optional

value of classical bits to control on, the classical controls are interpreted as an integer with lowest bit being the first one. If not specified, then the value is interpreted to be 2 ** len(classical_controls) - 1 (i.e. all classical controls are 1).

add_measurement(measurement, targets=None, index=None, classical_store=None)[source]

Adds a measurement with specified parameters to the circuit.

Parameters
name: string

Measurement name. If name is an instance of Measuremnent, parameters are unpacked and added.

targets: list

Gate targets

indexlist

classical_storeint

Classical register where result of measurement is stored.

add_state(state, targets=None, state_type='input')[source]

Add an input or ouput state to the circuit. By default all the input and output states will be initialized to None. A particular state can be added by specifying the state and the qubit where it has to be added along with the type as input or output.

Parameters
state: str

The state that has to be added. It can be any string such as 0, ‘+’, “A”, “Y”

targets: list

A list of qubit positions where the given state has to be added.

state_type: str

One of either “input” or “output”. This specifies whether the state to be added is an input or output. default: “input”

adjacent_gates()[source]

Method to resolve two qubit gates with non-adjacent control/s or target/s in terms of gates with adjacent interactions.

Returns
qubit_circuit: QubitCircuit

Return QubitCircuit of the gates for the qubit circuit with the resolved non-adjacent gates.

propagators(expand=True)[source]

Propagator matrix calculator for N qubits returning the individual steps as unitary matrices operating from left to right. :returns: U_list – Return list of unitary matrices for the qubit circuit. :rtype: list

propagators_no_expand()[source]

Propagator matrix calculator for N qubits returning the individual steps as unitary matrices operating from left to right.

Returns
U_listlist

Return list of unitary matrices for the qubit circuit.

remove_gate_or_measurement(index=None, end=None, name=None, remove='first')[source]

Remove a gate from a specific index or between two indexes or the first, last or all instances of a particular gate.

Parameters
indexint

Location of gate or measurement to be removed.

namestring

Gate or Measurement name to be removed.

removestring

If first or all gates/measurements are to be removed.

resolve_gates(basis=['CNOT', 'RX', 'RY', 'RZ'])[source]

Unitary matrix calculator for N qubits returning the individual steps as unitary matrices operating from left to right in the specified basis. Calls ‘_resolve_to_universal’ for each gate, this function maps each ‘GATENAME’ with its corresponding ‘_gate_basis_2q’ Subsequently calls _resolve_2q_basis for each basis, this function maps each ‘2QGATENAME’ with its corresponding ‘_basis_’

Parameters
basislist.

Basis of the resolved circuit.

Returns
qcQubitCircuit

Return QubitCircuit of resolved gates for the qubit circuit in the desired basis.

reverse_circuit()[source]

Reverse an entire circuit of unitary gates.

Returns
qubit_circuitQubitCircuit

Return QubitCircuit of resolved gates for the qubit circuit in the reverse order.

run(state, cbits=None, U_list=None, measure_results=None, precompute_unitary=False)[source]

Calculate the result of one instance of circuit run.

Parameters
stateket or oper

state vector or density matrix input.

cbitsList of ints, optional

initialization of the classical bits.

U_list: list of Qobj, optional

list of predefined unitaries corresponding to circuit.

measure_resultstuple of ints, optional

optional specification of each measurement result to enable post-selection. If specified, the measurement results are set to the tuple of bits (sequentially) instead of being chosen at random.

precompute_unitary: Boolean, optional

Specify if computation is done by pre-computing and aggregating gate unitaries. Possibly a faster method in the case of large number of repeat runs with different state inputs.

Returns
final_stateQobj

output state of the circuit run.

run_statistics(state, U_list=None, cbits=None, precompute_unitary=False)[source]

Calculate all the possible outputs of a circuit (varied by measurement gates).

Parameters
stateket or oper

state vector or density matrix input.

cbitsList of ints, optional

initialization of the classical bits.

U_list: list of Qobj, optional

list of predefined unitaries corresponding to circuit.

measure_resultstuple of ints, optional

optional specification of each measurement result to enable post-selection. If specified, the measurement results are set to the tuple of bits (sequentially) instead of being chosen at random.

precompute_unitary: Boolean, optional

Specify if computation is done by pre-computing and aggregating gate unitaries. Possibly a faster method in the case of large number of repeat runs with different state inputs.

Returns
result: CircuitResult

Return a CircuitResult object containing output states and and their probabilities.

class CircuitResult(final_states, probabilities, cbits=None)[source]
get_cbits(index=None)[source]

Return list of classical bit outputs corresponding to the results.

Parameters
index: int

Indicates i-th output, probability pair to be returned.

Returns
cbits: list of int or list of list of int

list of classical bit outputs

get_final_states(index=None)[source]

Return list of output states.

Parameters
index: int

Indicates i-th state to be returned.

Returns
final_states: Qobj or list of Qobj.

List of output kets or density matrices.

get_probabilities(index=None)[source]

Return list of probabilities corresponding to the output states.

Parameters
index: int

Indicates i-th probability to be returned.

Returns
probabilities: float or list of float

Probabilities associated with each output state.

class CircuitSimulator(qc, state=None, cbits=None, U_list=None, measure_results=None, mode='state_vector_simulator', precompute_unitary=False)[source]
initialize(state=None, cbits=None, measure_results=None)[source]

Reset Simulator state variables to start a new run.

Parameters
state: ket or oper

ket or density matrix

cbits: list of int, optional

initial value of classical bits

U_list: list of Qobj, optional

list of predefined unitaries corresponding to circuit.

measure_resultstuple of ints, optional

optional specification of each measurement result to enable post-selection. If specified, the measurement results are set to the tuple of bits (sequentially) instead of being chosen at random.

run(state, cbits=None, measure_results=None)[source]

Calculate the result of one instance of circuit run.

Parameters
stateket or oper

state vector or density matrix input.

cbitsList of ints, optional

initialization of the classical bits.

measure_resultstuple of ints, optional

optional specification of each measurement result to enable post-selection. If specified, the measurement results are set to the tuple of bits (sequentially) instead of being chosen at random.

Returns
result: CircuitResult

Return a CircuitResult object containing output state and probability.

run_statistics(state, cbits=None)[source]

Calculate all the possible outputs of a circuit (varied by measurement gates).

Parameters
stateket

state to be observed on specified by density matrix.

cbitsList of ints, optional

initialization of the classical bits.

Returns
result: CircuitResult

Return a CircuitResult object containing output states and and their probabilities.

step()[source]

Return state after one step of circuit evolution (gate or measurement).

Returns
stateket or oper

state after one evolution step.

class Processor(N, t1=None, t2=None, dims=None, spline_kind='step_func')[source]

A simulator of a quantum device based on the QuTiP solver qutip.mesolve. It is defined by the available driving Hamiltonian and the decoherence time for each component systems. The processor can simulate the evolution under the given control pulses. Noisy evolution is supported by Noise and can be added to the processor.

Parameters
N: int

The number of component systems.

t1: list or float, optional

Characterize the decoherence of amplitude damping for each qubit. A list of size N or a float for all qubits.

t2: list of float, optional

Characterize the decoherence of dephasing for each qubit. A list of size N or a float for all qubits.

dims: list, optional

The dimension of each component system. Default value is a qubit system of dim=[2,2,2,...,2]

spline_kind: str, optional

Type of the coefficient interpolation. Default is “step_func” Note that they have different requirement for the length of coeff.

• “step_func”: The coefficient will be treated as a step function. E.g. tlist=[0,1,2] and coeff=[3,2], means that the coefficient is 3 in t=[0,1) and 2 in t=[2,3). It requires len(coeff)=len(tlist)-1 or len(coeff)=len(tlist), but in the second case the last element of coeff has no effect.

• “cubic”: Use cubic interpolation for the coefficient. It requires len(coeff)=len(tlist)

Attributes
N: int

The number of component systems.

pulses: list of :class:.Pulse

A list of control pulses of this device

t1: float or list

Characterize the decoherence of amplitude damping of each qubit.

t2: float or list

Characterize the decoherence of dephasing for each qubit.

noise: :class:.Noise, optional

A list of noise objects. They will be processed when creating the noisy qutip.QobjEvo from the processor or run the simulation.

drift: :class:qutip.qip.pulse.Drift

A Drift object representing the drift Hamiltonians.

dims: list

The dimension of each component system. Default value is a qubit system of dim=[2,2,2,...,2]

spline_kind: str

Type of the coefficient interpolation. See parameters of Processor for details.

add_control(qobj, targets=None, cyclic_permutation=False, label=None)[source]

Add a control Hamiltonian to the processor. It creates a new Pulse object for the device that is turned off (tlist = None, coeff = None). To activate the pulse, one can set its tlist and coeff.

Parameters
qobj: :class:qutip.Qobj

The Hamiltonian for the control pulse..

targets: list, optional

The indices of the target qubits (or subquantum system of other dimensions).

cyclic_permutation: bool, optional

If true, the Hamiltonian will be expanded for all cyclic permutation of the target qubits.

label: str, optional

The label (name) of the pulse

add_drift(qobj, targets, cyclic_permutation=False)[source]

Add a drift Hamiltonians. The drift Hamiltonians are intrinsic of the quantum system and cannot be controlled by external field.

Parameters
qobj: :class:qutip.Qobj

The drift Hamiltonian.

targets: list

The indices of the target qubits (or subquantum system of other dimensions).

add_noise(noise)[source]

Add a noise object to the processor

Parameters
noise: :class:.Noise

The noise object defined outside the processor

add_pulse(pulse)[source]

Add a new pulse to the device.

Parameters
pulse: :class:.Pulse

property coeffs

A list of the coefficients for all control pulses.

property ctrls

A list of Hamiltonians of all pulses.

eliminate_auxillary_modes(U)[source]

Eliminate the auxillary modes like the cavity modes in cqed. (Defined in subclasses)

get_full_coeffs(full_tlist=None)[source]

Return the full coefficients in a 2d matrix form. Each row corresponds to one pulse. If the tlist are different for different pulses, the length of each row will be same as the full_tlist (see method get_full_tlist). Interpolation is used for adding the missing coefficient according to spline_kind.

Returns
coeffs: array-like 2d

The coefficients for all ideal pulses.

get_full_tlist(tol=1e-10)[source]

Return the full tlist of the ideal pulses. If different pulses have different time steps, it will collect all the time steps in a sorted array.

Returns
full_tlist: array-like 1d

The full time sequence for the ideal evolution.

get_noisy_pulses(device_noise=False, drift=False)[source]

It takes the pulses defined in the Processor and adds noise according to Processor.noise. It does not modify the pulses saved in Processor.pulses but returns a new list. The length of the new list of noisy pulses might be longer because of drift Hamiltonian and device noise. They will be added to the end of the pulses list.

Parameters
device_noise: bool, optional

If true, include pulse independent noise such as single qubit Relaxation. Default is False.

drift: bool, optional

If true, include drift Hamiltonians. Default is False.

Returns
noisy_pulses: list of Pulse

A list of noisy pulses.

get_operators_labels()[source]

Get the labels for each Hamiltonian. It is used in the methodplot_pulses. It is a 2-d nested list, in the plot, a different color will be used for each sublist.

get_qobjevo(args=None, noisy=False)[source]

Create a qutip.QobjEvo representation of the evolution. It calls the method get_noisy_pulses and create the QobjEvo from it.

Parameters
args: dict, optional

Arguments for qutip.QobjEvo

noisy: bool, optional

If noise are included. Default is False.

Returns
qobjevo: qutip.QobjEvo

The qutip.QobjEvo representation of the unitary evolution.

c_ops: list of qutip.QobjEvo

A list of lindblad operators is also returned. if noisy==Flase, it is always an empty list.

load_circuit(qc)[source]

Translate an QubitCircuit to its corresponding Hamiltonians. (Defined in subclasses)

plot_pulses(title=None, figsize=(12, 6), dpi=None, show_axis=False, rescale_pulse_coeffs=True, num_steps=1000)[source]

Plot the ideal pulse coefficients.

Parameters
title: str, optional

Title for the plot.

figsize: tuple, optional

The size of the figure.

dpi: int, optional

The dpi of the figure.

show_axis: bool, optional

If the axis are shown.

rescale_pulse_coeffs: bool, optional

Rescale the hight of each pulses.

num_steps: int, optional

Number of time steps in the plot.

Returns
fig: matplotlib.figure.Figure

The Figure object for the plot.

ax: matplotlib.axes._subplots.AxesSubplot

The axes for the plot.

Notes

plot_pulses only works for array_like coefficients

read_coeff(file_name, inctime=True)[source]

Read the control amplitudes matrix and time list saved in the file by save_amp.

Parameters
file_name: string

Name of the file.

inctime: bool, optional

True if the time list in included in the first column.

Returns
tlist: array_like

The time list read from the file.

coeffs: array_like

The pulse matrix read from the file.

remove_pulse(indices=None, label=None)[source]

Remove the control pulse with given indices.

Parameters
indices: int or list of int

The indices of the control Hamiltonians to be removed.

label: str

The label of the pulse

run(qc=None)[source]

Calculate the propagator of the evolution by matrix exponentiation. This method won’t include noise or collpase.

Parameters
qc: :class:.QubitCircuit, optional

Takes the quantum circuit to be implemented. If not given, use the quantum circuit saved in the processor by load_circuit.

Returns
U_list: list

The propagator matrix obtained from the physical implementation.

run_analytically(init_state=None, qc=None)[source]

Simulate the state evolution under the given qutip.QubitCircuit with matrice exponentiation. It will calculate the propagator with matrix exponentiation and return a list of qutip.Qobj. This method won’t include noise or collpase.

Parameters
qc: :class:.QubitCircuit, optional

Takes the quantum circuit to be implemented. If not given, use the quantum circuit saved in the processor by load_circuit.

init_state: :class:qutip.Qobj, optional

The initial state of the qubits in the register.

Returns
U_list: list

A list of propagators obtained for the physical implementation.

run_state(init_state=None, analytical=False, states=None, noisy=True, solver='mesolve', **kwargs)[source]

If analytical is False, use qutip.mesolve to calculate the time of the state evolution and return the result. Other arguments of mesolve can be given as keyword arguments.

If analytical is True, calculate the propagator with matrix exponentiation and return a list of matrices. Noise will be neglected in this option.

Parameters
init_state: Qobj

Initial density matrix or state vector (ket).

analytical: bool

If True, calculate the evolution with matrices exponentiation.

states: :class:qutip.Qobj, optional

Old API, same as init_state.

solver: str

“mesolve” or “mcsolve”

**kwargs

Keyword arguments for the qutip solver.

Returns
evo_result: qutip.Result

If analytical is False, an instance of the class qutip.Result will be returned.

If analytical is True, a list of matrices representation is returned.

save_coeff(file_name, inctime=True)[source]

Save a file with the control amplitudes in each timeslot.

Parameters
file_name: string

Name of the file.

inctime: bool, optional

True if the time list should be included in the first column.

set_all_tlist(tlist)[source]

Set the same tlist for all the pulses.

Parameters
tlist: array-like, optional

A list of time at which the time-dependent coefficients are applied. See Pulse for detailed information

class OptPulseProcessor(N, drift=None, t1=None, t2=None, dims=None)[source]

A processor, which takes the Hamiltonian available as dynamic generators, calls the qutip.control.optimize_pulse_unitary function to find an optimized pulse sequence for the desired quantum circuit. The processor can simulate the evolution under the given control pulses using qutip.mesolve. (For attributes documentation, please refer to the parent class Processor)

Parameters
N: int

The number of component systems.

drift: :class:qutip.Qobj

The drift Hamiltonian. The size must match the whole quantum system.

t1: list or float

Characterize the decoherence of amplitude damping for each qubit. A list of size N or a float for all qubits.

t2: list of float

Characterize the decoherence of dephasing for each qubit. A list of size N or a float for all qubits.

dims: list

The dimension of each component system. Default value is a qubit system of dim=[2,2,2,...,2]

add_control(qobj, targets=None, cyclic_permutation=False, label=None)

Add a control Hamiltonian to the processor. It creates a new Pulse object for the device that is turned off (tlist = None, coeff = None). To activate the pulse, one can set its tlist and coeff.

Parameters
qobj: :class:qutip.Qobj

The Hamiltonian for the control pulse..

targets: list, optional

The indices of the target qubits (or subquantum system of other dimensions).

cyclic_permutation: bool, optional

If true, the Hamiltonian will be expanded for all cyclic permutation of the target qubits.

label: str, optional

The label (name) of the pulse

add_drift(qobj, targets, cyclic_permutation=False)

Add a drift Hamiltonians. The drift Hamiltonians are intrinsic of the quantum system and cannot be controlled by external field.

Parameters
qobj: :class:qutip.Qobj

The drift Hamiltonian.

targets: list

The indices of the target qubits (or subquantum system of other dimensions).

add_noise(noise)

Add a noise object to the processor

Parameters
noise: :class:.Noise

The noise object defined outside the processor

add_pulse(pulse)

Add a new pulse to the device.

Parameters
pulse: :class:.Pulse

property coeffs

A list of the coefficients for all control pulses.

property ctrls

A list of Hamiltonians of all pulses.

eliminate_auxillary_modes(U)

Eliminate the auxillary modes like the cavity modes in cqed. (Defined in subclasses)

get_full_coeffs(full_tlist=None)

Return the full coefficients in a 2d matrix form. Each row corresponds to one pulse. If the tlist are different for different pulses, the length of each row will be same as the full_tlist (see method get_full_tlist). Interpolation is used for adding the missing coefficient according to spline_kind.

Returns
coeffs: array-like 2d

The coefficients for all ideal pulses.

get_full_tlist(tol=1e-10)

Return the full tlist of the ideal pulses. If different pulses have different time steps, it will collect all the time steps in a sorted array.

Returns
full_tlist: array-like 1d

The full time sequence for the ideal evolution.

get_noisy_pulses(device_noise=False, drift=False)

It takes the pulses defined in the Processor and adds noise according to Processor.noise. It does not modify the pulses saved in Processor.pulses but returns a new list. The length of the new list of noisy pulses might be longer because of drift Hamiltonian and device noise. They will be added to the end of the pulses list.

Parameters
device_noise: bool, optional

If true, include pulse independent noise such as single qubit Relaxation. Default is False.

drift: bool, optional

If true, include drift Hamiltonians. Default is False.

Returns
noisy_pulses: list of Pulse

A list of noisy pulses.

get_operators_labels()

Get the labels for each Hamiltonian. It is used in the methodplot_pulses. It is a 2-d nested list, in the plot, a different color will be used for each sublist.

get_qobjevo(args=None, noisy=False)

Create a qutip.QobjEvo representation of the evolution. It calls the method get_noisy_pulses and create the QobjEvo from it.

Parameters
args: dict, optional

Arguments for qutip.QobjEvo

noisy: bool, optional

If noise are included. Default is False.

Returns
qobjevo: qutip.QobjEvo

The qutip.QobjEvo representation of the unitary evolution.

c_ops: list of qutip.QobjEvo

A list of lindblad operators is also returned. if noisy==Flase, it is always an empty list.

load_circuit(qc, min_fid_err=inf, merge_gates=True, setting_args=None, verbose=False, **kwargs)[source]

Find the pulses realizing a given QubitCircuit using qutip.control.optimize_pulse_unitary. Further parameter for for qutip.control.optimize_pulse_unitary needs to be given as keyword arguments. By default, it first merge all the gates into one unitary and then find the control pulses for it. It can be turned off and one can set different parameters for different gates. See examples for details.

Parameters
qc: :class:.QubitCircuit or list of Qobj

The quantum circuit to be translated.

min_fid_err: float, optional

The minimal fidelity tolerance, if the fidelity error of any gate decomposition is higher, a warning will be given. Default is infinite.

merge_gates: boolean, optimal

If True, merge all gate/Qobj into one Qobj and then find the optimal pulses for this unitary matrix. If False, find the optimal pulses for each gate/Qobj.

setting_args: dict, optional

Only considered if merge_gates is False. It is a dictionary containing keyword arguments for different gates.

E.g.:

setting_args = {"SNOT": {"num_tslots": 10, "evo_time": 1},
"SWAP": {"num_tslots": 30, "evo_time": 3},
"CNOT": {"num_tslots": 30, "evo_time": 3}}

verbose: boolean, optional

If true, the information for each decomposed gate will be shown. Default is False.

**kwargs

keyword arguments for qutip.control.optimize_pulse_unitary

Returns
tlist: array_like

A NumPy array specifies the time of each coefficient

coeffs: array_like

A 2d NumPy array of the shape (len(ctrls), len(tlist)-1). Each row corresponds to the control pulse sequence for one Hamiltonian.

Notes

len(tlist) - 1 = coeffs.shape[1] since tlist gives the beginning and the end of the pulses.

Examples

Same parameter for all the gates:

qc = QubitCircuit(N=1)
num_tslots = 10
evo_time = 10
processor = OptPulseProcessor(N=1, drift=sigmaz(),
ctrls=[sigmax()])
# num_tslots and evo_time are two keyword arguments
qc, num_tslots=num_tslots, evo_time=evo_time)


Different parameters for different gates:

qc = QubitCircuit(N=2)

processor = OptPulseProcessor(N=2, drift=tensor([sigmaz()]*2))
setting_args = {"SNOT": {"num_tslots": 10, "evo_time": 1},
"SWAP": {"num_tslots": 30, "evo_time": 3},
"CNOT": {"num_tslots": 30, "evo_time": 3}}
setting_args=setting_args,
merge_gates=False)

plot_pulses(title=None, figsize=(12, 6), dpi=None, show_axis=False, rescale_pulse_coeffs=True, num_steps=1000)

Plot the ideal pulse coefficients.

Parameters
title: str, optional

Title for the plot.

figsize: tuple, optional

The size of the figure.

dpi: int, optional

The dpi of the figure.

show_axis: bool, optional

If the axis are shown.

rescale_pulse_coeffs: bool, optional

Rescale the hight of each pulses.

num_steps: int, optional

Number of time steps in the plot.

Returns
fig: matplotlib.figure.Figure

The Figure object for the plot.

ax: matplotlib.axes._subplots.AxesSubplot

The axes for the plot.

Notes

plot_pulses only works for array_like coefficients

read_coeff(file_name, inctime=True)

Read the control amplitudes matrix and time list saved in the file by save_amp.

Parameters
file_name: string

Name of the file.

inctime: bool, optional

True if the time list in included in the first column.

Returns
tlist: array_like

The time list read from the file.

coeffs: array_like

The pulse matrix read from the file.

remove_pulse(indices=None, label=None)

Remove the control pulse with given indices.

Parameters
indices: int or list of int

The indices of the control Hamiltonians to be removed.

label: str

The label of the pulse

run(qc=None)

Calculate the propagator of the evolution by matrix exponentiation. This method won’t include noise or collpase.

Parameters
qc: :class:.QubitCircuit, optional

Takes the quantum circuit to be implemented. If not given, use the quantum circuit saved in the processor by load_circuit.

Returns
U_list: list

The propagator matrix obtained from the physical implementation.

run_analytically(init_state=None, qc=None)

Simulate the state evolution under the given qutip.QubitCircuit with matrice exponentiation. It will calculate the propagator with matrix exponentiation and return a list of qutip.Qobj. This method won’t include noise or collpase.

Parameters
qc: :class:.QubitCircuit, optional

Takes the quantum circuit to be implemented. If not given, use the quantum circuit saved in the processor by load_circuit.

init_state: :class:qutip.Qobj, optional

The initial state of the qubits in the register.

Returns
U_list: list

A list of propagators obtained for the physical implementation.

run_state(init_state=None, analytical=False, states=None, noisy=True, solver='mesolve', **kwargs)

If analytical is False, use qutip.mesolve to calculate the time of the state evolution and return the result. Other arguments of mesolve can be given as keyword arguments.

If analytical is True, calculate the propagator with matrix exponentiation and return a list of matrices. Noise will be neglected in this option.

Parameters
init_state: Qobj

Initial density matrix or state vector (ket).

analytical: bool

If True, calculate the evolution with matrices exponentiation.

states: :class:qutip.Qobj, optional

Old API, same as init_state.

solver: str

“mesolve” or “mcsolve”

**kwargs

Keyword arguments for the qutip solver.

Returns
evo_result: qutip.Result

If analytical is False, an instance of the class qutip.Result will be returned.

If analytical is True, a list of matrices representation is returned.

save_coeff(file_name, inctime=True)

Save a file with the control amplitudes in each timeslot.

Parameters
file_name: string

Name of the file.

inctime: bool, optional

True if the time list should be included in the first column.

set_all_tlist(tlist)

Set the same tlist for all the pulses.

Parameters
tlist: array-like, optional

A list of time at which the time-dependent coefficients are applied. See Pulse for detailed information

class ModelProcessor(N, correct_global_phase=True, t1=None, t2=None)[source]

The base class for a circuit processor simulating a physical device, e.g cavityQED, spinchain. The available Hamiltonian of the system is predefined. The processor can simulate the evolution under the given control pulses either numerically or analytically. It cannot be used alone, please refer to the sub-classes. (Only additional attributes are documented here, for others please refer to the parent class Processor)

Parameters
N: int

The number of component systems.

correct_global_phase: boolean, optional

If true, the analytical solution will track the global phase. It has no effect on the numerical solution.

t1: list or float

Characterize the decoherence of amplitude damping for each qubit. A list of size N or a float for all qubits.

t2: list of float

Characterize the decoherence of dephasing for each qubit. A list of size N or a float for all qubits.

Attributes
params: dict

A Python dictionary contains the name and the value of the parameters in the physical realization, such as laser frequency, detuning etc.

correct_global_phase: float

Save the global phase, the analytical solution will track the global phase. It has no effect on the numerical solution.

add_control(qobj, targets=None, cyclic_permutation=False, label=None)

Add a control Hamiltonian to the processor. It creates a new Pulse object for the device that is turned off (tlist = None, coeff = None). To activate the pulse, one can set its tlist and coeff.

Parameters
qobj: :class:qutip.Qobj

The Hamiltonian for the control pulse..

targets: list, optional

The indices of the target qubits (or subquantum system of other dimensions).

cyclic_permutation: bool, optional

If true, the Hamiltonian will be expanded for all cyclic permutation of the target qubits.

label: str, optional

The label (name) of the pulse

add_drift(qobj, targets, cyclic_permutation=False)

Add a drift Hamiltonians. The drift Hamiltonians are intrinsic of the quantum system and cannot be controlled by external field.

Parameters
qobj: :class:qutip.Qobj

The drift Hamiltonian.

targets: list

The indices of the target qubits (or subquantum system of other dimensions).

add_noise(noise)

Add a noise object to the processor

Parameters
noise: :class:.Noise

The noise object defined outside the processor

add_pulse(pulse)

Add a new pulse to the device.

Parameters
pulse: :class:.Pulse

property coeffs

A list of the coefficients for all control pulses.

property ctrls

A list of Hamiltonians of all pulses.

eliminate_auxillary_modes(U)

Eliminate the auxillary modes like the cavity modes in cqed. (Defined in subclasses)

get_full_coeffs(full_tlist=None)

Return the full coefficients in a 2d matrix form. Each row corresponds to one pulse. If the tlist are different for different pulses, the length of each row will be same as the full_tlist (see method get_full_tlist). Interpolation is used for adding the missing coefficient according to spline_kind.

Returns
coeffs: array-like 2d

The coefficients for all ideal pulses.

get_full_tlist(tol=1e-10)

Return the full tlist of the ideal pulses. If different pulses have different time steps, it will collect all the time steps in a sorted array.

Returns
full_tlist: array-like 1d

The full time sequence for the ideal evolution.

get_noisy_pulses(device_noise=False, drift=False)

It takes the pulses defined in the Processor and adds noise according to Processor.noise. It does not modify the pulses saved in Processor.pulses but returns a new list. The length of the new list of noisy pulses might be longer because of drift Hamiltonian and device noise. They will be added to the end of the pulses list.

Parameters
device_noise: bool, optional

If true, include pulse independent noise such as single qubit Relaxation. Default is False.

drift: bool, optional

If true, include drift Hamiltonians. Default is False.

Returns
noisy_pulses: list of Pulse

A list of noisy pulses.

get_operators_labels()

Get the labels for each Hamiltonian. It is used in the methodplot_pulses. It is a 2-d nested list, in the plot, a different color will be used for each sublist.

get_ops_and_u()[source]

Get the labels for each Hamiltonian.

Returns
ctrls: list

The list of Hamiltonians

coeffs: array_like

The transposed pulse matrix

get_qobjevo(args=None, noisy=False)

Create a qutip.QobjEvo representation of the evolution. It calls the method get_noisy_pulses and create the QobjEvo from it.

Parameters
args: dict, optional

Arguments for qutip.QobjEvo

noisy: bool, optional

If noise are included. Default is False.

Returns
qobjevo: qutip.QobjEvo

The qutip.QobjEvo representation of the unitary evolution.

c_ops: list of qutip.QobjEvo

A list of lindblad operators is also returned. if noisy==Flase, it is always an empty list.

load_circuit(qc)

Translate an QubitCircuit to its corresponding Hamiltonians. (Defined in subclasses)

plot_pulses(title=None, figsize=(12, 6), dpi=None, show_axis=False, rescale_pulse_coeffs=True, num_steps=1000)

Plot the ideal pulse coefficients.

Parameters
title: str, optional

Title for the plot.

figsize: tuple, optional

The size of the figure.

dpi: int, optional

The dpi of the figure.

show_axis: bool, optional

If the axis are shown.

rescale_pulse_coeffs: bool, optional

Rescale the hight of each pulses.

num_steps: int, optional

Number of time steps in the plot.

Returns
fig: matplotlib.figure.Figure

The Figure object for the plot.

ax: matplotlib.axes._subplots.AxesSubplot

The axes for the plot.

Notes

plot_pulses only works for array_like coefficients

pulse_matrix(dt=0.01)[source]

Generates the pulse matrix for the desired physical system.

Returns
t, u, labels:

Returns the total time and label for every operation.

read_coeff(file_name, inctime=True)

Read the control amplitudes matrix and time list saved in the file by save_amp.

Parameters
file_name: string

Name of the file.

inctime: bool, optional

True if the time list in included in the first column.

Returns
tlist: array_like

The time list read from the file.

coeffs: array_like

The pulse matrix read from the file.

remove_pulse(indices=None, label=None)

Remove the control pulse with given indices.

Parameters
indices: int or list of int

The indices of the control Hamiltonians to be removed.

label: str

The label of the pulse

run(qc=None)

Calculate the propagator of the evolution by matrix exponentiation. This method won’t include noise or collpase.

Parameters
qc: :class:.QubitCircuit, optional

Takes the quantum circuit to be implemented. If not given, use the quantum circuit saved in the processor by load_circuit.

Returns
U_list: list

The propagator matrix obtained from the physical implementation.

run_analytically(init_state=None, qc=None)

Simulate the state evolution under the given qutip.QubitCircuit with matrice exponentiation. It will calculate the propagator with matrix exponentiation and return a list of qutip.Qobj. This method won’t include noise or collpase.

Parameters
qc: :class:.QubitCircuit, optional

Takes the quantum circuit to be implemented. If not given, use the quantum circuit saved in the processor by load_circuit.

init_state: :class:qutip.Qobj, optional

The initial state of the qubits in the register.

Returns
U_list: list

A list of propagators obtained for the physical implementation.

run_state(init_state=None, analytical=False, qc=None, states=None, **kwargs)[source]

If analytical is False, use qutip.mesolve to calculate the time of the state evolution and return the result. Other arguments of mesolve can be given as keyword arguments. If analytical is True, calculate the propagator with matrix exponentiation and return a list of matrices.

Parameters
init_state: Qobj

Initial density matrix or state vector (ket).

analytical: boolean

If True, calculate the evolution with matrices exponentiation.

qc: :class:.QubitCircuit, optional

A quantum circuit. If given, it first calls the load_circuit and then calculate the evolution.

states: :class:qutip.Qobj, optional

Old API, same as init_state.

**kwargs

Keyword arguments for the qutip solver.

Returns
evo_result: qutip.Result

If analytical is False, an instance of the class qutip.Result will be returned.

If analytical is True, a list of matrices representation is returned.

save_coeff(file_name, inctime=True)

Save a file with the control amplitudes in each timeslot.

Parameters
file_name: string

Name of the file.

inctime: bool, optional

True if the time list should be included in the first column.

set_all_tlist(tlist)

Set the same tlist for all the pulses.

Parameters
tlist: array-like, optional

A list of time at which the time-dependent coefficients are applied. See Pulse for detailed information

set_up_params()[source]

Save the parameters in the attribute params and check the validity. (Defined in subclasses)

Notes

All parameters will be multiplied by 2*pi for simplicity

to_array(params, N)[source]

Transfer a parameter to an array.

class SpinChain(N, correct_global_phase, sx, sz, sxsy, t1, t2)[source]

The processor based on the physical implementation of a spin chain qubits system. The available Hamiltonian of the system is predefined. The processor can simulate the evolution under the given control pulses either numerically or analytically. It is a base class and should not be used directly, please refer the the subclasses qutip.qip.device.LinearSpinChain and qutip.qip.device.CircularSpinChain. (Only additional attributes are documented here, for others please refer to the parent class ModelProcessor)

Parameters
N: int

The number of qubits in the system.

correct_global_phase: float

Save the global phase, the analytical solution will track the global phase. It has no effect on the numerical solution.

sx: int or list

The delta for each of the qubits in the system.

sz: int or list

The epsilon for each of the qubits in the system.

sxsy: int or list

The interaction strength for each of the qubit pair in the system.

t1: list or float

Characterize the decoherence of amplitude damping for each qubit. A list of size N or a float for all qubits.

t2: list of float

Characterize the decoherence of dephasing for each qubit. A list of size N or a float for all qubits.

Attributes
sx: list

The delta for each of the qubits in the system.

sz: list

The epsilon for each of the qubits in the system.

sxsy: list

The interaction strength for each of the qubit pair in the system.

sx_ops: list

A list of sigmax Hamiltonians for each qubit.

sz_ops: list

A list of sigmaz Hamiltonians for each qubit.

sxsy_ops: list

A list of tensor(sigmax, sigmay) interacting Hamiltonians for each qubit.

sx_u: array_like

Pulse matrix for sigmax Hamiltonians.

sz_u: array_like

Pulse matrix for sigmaz Hamiltonians.

sxsy_u: array_like

Pulse matrix for tensor(sigmax, sigmay) interacting Hamiltonians.

add_control(qobj, targets=None, cyclic_permutation=False, label=None)

Add a control Hamiltonian to the processor. It creates a new Pulse object for the device that is turned off (tlist = None, coeff = None). To activate the pulse, one can set its tlist and coeff.

Parameters
qobj: :class:qutip.Qobj

The Hamiltonian for the control pulse..

targets: list, optional

The indices of the target qubits (or subquantum system of other dimensions).

cyclic_permutation: bool, optional

If true, the Hamiltonian will be expanded for all cyclic permutation of the target qubits.

label: str, optional

The label (name) of the pulse

add_drift(qobj, targets, cyclic_permutation=False)

Add a drift Hamiltonians. The drift Hamiltonians are intrinsic of the quantum system and cannot be controlled by external field.

Parameters
qobj: :class:qutip.Qobj

The drift Hamiltonian.

targets: list

The indices of the target qubits (or subquantum system of other dimensions).

add_noise(noise)

Add a noise object to the processor

Parameters
noise: :class:.Noise

The noise object defined outside the processor

add_pulse(pulse)

Add a new pulse to the device.

Parameters
pulse: :class:.Pulse

adjacent_gates(qc, setup='linear')[source]

Method to resolve 2 qubit gates with non-adjacent control/s or target/s in terms of gates with adjacent interactions for linear/circular spin chain system.

Parameters
qc: :class:.QubitCircuit

The circular spin chain circuit to be resolved

setup: Boolean

Linear of Circular spin chain setup

Returns
qc: QubitCircuit

Returns QubitCircuit of resolved gates for the qubit circuit in the desired basis.

property coeffs

A list of the coefficients for all control pulses.

property ctrls

A list of Hamiltonians of all pulses.

eliminate_auxillary_modes(U)[source]

Eliminate the auxillary modes like the cavity modes in cqed. (Defined in subclasses)

get_full_coeffs(full_tlist=None)

Return the full coefficients in a 2d matrix form. Each row corresponds to one pulse. If the tlist are different for different pulses, the length of each row will be same as the full_tlist (see method get_full_tlist). Interpolation is used for adding the missing coefficient according to spline_kind.

Returns
coeffs: array-like 2d

The coefficients for all ideal pulses.

get_full_tlist(tol=1e-10)

Return the full tlist of the ideal pulses. If different pulses have different time steps, it will collect all the time steps in a sorted array.

Returns
full_tlist: array-like 1d

The full time sequence for the ideal evolution.

get_noisy_pulses(device_noise=False, drift=False)

It takes the pulses defined in the Processor and adds noise according to Processor.noise. It does not modify the pulses saved in Processor.pulses but returns a new list. The length of the new list of noisy pulses might be longer because of drift Hamiltonian and device noise. They will be added to the end of the pulses list.

Parameters
device_noise: bool, optional

If true, include pulse independent noise such as single qubit Relaxation. Default is False.

drift: bool, optional

If true, include drift Hamiltonians. Default is False.

Returns
noisy_pulses: list of Pulse

A list of noisy pulses.

get_operators_labels()

Get the labels for each Hamiltonian. It is used in the methodplot_pulses. It is a 2-d nested list, in the plot, a different color will be used for each sublist.

get_ops_and_u()

Get the labels for each Hamiltonian.

Returns
ctrls: list

The list of Hamiltonians

coeffs: array_like

The transposed pulse matrix

get_qobjevo(args=None, noisy=False)

Create a qutip.QobjEvo representation of the evolution. It calls the method get_noisy_pulses and create the QobjEvo from it.

Parameters
args: dict, optional

Arguments for qutip.QobjEvo

noisy: bool, optional

If noise are included. Default is False.

Returns
qobjevo: qutip.QobjEvo

The qutip.QobjEvo representation of the unitary evolution.

c_ops: list of qutip.QobjEvo

A list of lindblad operators is also returned. if noisy==Flase, it is always an empty list.

load_circuit(qc, setup, schedule_mode='ASAP', compiler=None)[source]

Decompose a QubitCircuit in to the control amplitude generating the corresponding evolution.

Parameters
qc: :class:.QubitCircuit

Takes the quantum circuit to be implemented.

setup: string

“linear” or “circular” for two sub-classes.

Returns
tlist: array_like

A NumPy array specifies the time of each coefficient

coeffs: array_like

A 2d NumPy array of the shape (len(ctrls), len(tlist)). Each row corresponds to the control pulse sequence for one Hamiltonian.

optimize_circuit(qc)[source]

Take a quantum circuit/algorithm and convert it into the optimal form/basis for the desired physical system.

Parameters
qc: :class:.QubitCircuit

Takes the quantum circuit to be implemented.

Returns
qc: QubitCircuit

The circuit representation with elementary gates that can be implemented in this model.

plot_pulses(title=None, figsize=(12, 6), dpi=None, show_axis=False, rescale_pulse_coeffs=True, num_steps=1000)

Plot the ideal pulse coefficients.

Parameters
title: str, optional

Title for the plot.

figsize: tuple, optional

The size of the figure.

dpi: int, optional

The dpi of the figure.

show_axis: bool, optional

If the axis are shown.

rescale_pulse_coeffs: bool, optional

Rescale the hight of each pulses.

num_steps: int, optional

Number of time steps in the plot.

Returns
fig: matplotlib.figure.Figure

The Figure object for the plot.

ax: matplotlib.axes._subplots.AxesSubplot

The axes for the plot.

Notes

plot_pulses only works for array_like coefficients

pulse_matrix(dt=0.01)

Generates the pulse matrix for the desired physical system.

Returns
t, u, labels:

Returns the total time and label for every operation.

read_coeff(file_name, inctime=True)

Read the control amplitudes matrix and time list saved in the file by save_amp.

Parameters
file_name: string

Name of the file.

inctime: bool, optional

True if the time list in included in the first column.

Returns
tlist: array_like

The time list read from the file.

coeffs: array_like

The pulse matrix read from the file.

remove_pulse(indices=None, label=None)

Remove the control pulse with given indices.

Parameters
indices: int or list of int

The indices of the control Hamiltonians to be removed.

label: str

The label of the pulse

run(qc=None)

Calculate the propagator of the evolution by matrix exponentiation. This method won’t include noise or collpase.

Parameters
qc: :class:.QubitCircuit, optional

Takes the quantum circuit to be implemented. If not given, use the quantum circuit saved in the processor by load_circuit.

Returns
U_list: list

The propagator matrix obtained from the physical implementation.

run_analytically(init_state=None, qc=None)

Simulate the state evolution under the given qutip.QubitCircuit with matrice exponentiation. It will calculate the propagator with matrix exponentiation and return a list of qutip.Qobj. This method won’t include noise or collpase.

Parameters
qc: :class:.QubitCircuit, optional

Takes the quantum circuit to be implemented. If not given, use the quantum circuit saved in the processor by load_circuit.

init_state: :class:qutip.Qobj, optional

The initial state of the qubits in the register.

Returns
U_list: list

A list of propagators obtained for the physical implementation.

run_state(init_state=None, analytical=False, qc=None, states=None, **kwargs)

If analytical is False, use qutip.mesolve to calculate the time of the state evolution and return the result. Other arguments of mesolve can be given as keyword arguments. If analytical is True, calculate the propagator with matrix exponentiation and return a list of matrices.

Parameters
init_state: Qobj

Initial density matrix or state vector (ket).

analytical: boolean

If True, calculate the evolution with matrices exponentiation.

qc: :class:.QubitCircuit, optional

A quantum circuit. If given, it first calls the load_circuit and then calculate the evolution.

states: :class:qutip.Qobj, optional

Old API, same as init_state.

**kwargs

Keyword arguments for the qutip solver.

Returns
evo_result: qutip.Result

If analytical is False, an instance of the class qutip.Result will be returned.

If analytical is True, a list of matrices representation is returned.

save_coeff(file_name, inctime=True)

Save a file with the control amplitudes in each timeslot.

Parameters
file_name: string

Name of the file.

inctime: bool, optional

True if the time list should be included in the first column.

set_all_tlist(tlist)

Set the same tlist for all the pulses.

Parameters
tlist: array-like, optional

A list of time at which the time-dependent coefficients are applied. See Pulse for detailed information

set_up_ops(N)[source]

Generate the Hamiltonians for the spinchain model and save them in the attribute ctrls.

Parameters
N: int

The number of qubits in the system.

set_up_params(sx, sz)[source]

Save the parameters in the attribute params and check the validity. The keys of params including “sx”, “sz”, and “sxsy”, each mapped to a list for parameters corresponding to each qubits. For coupling strength “sxsy”, list element i is the interaction between qubits i and i+1.

Parameters
sx: float or list

The coefficient of sigmax in the model

sz: flaot or list

The coefficient of sigmaz in the model

Notes

The coefficient of sxsy is defined in the submethods. All parameters will be multiplied by 2*pi for simplicity

to_array(params, N)

Transfer a parameter to an array.

class LinearSpinChain(N, correct_global_phase=True, sx=0.25, sz=1.0, sxsy=0.1, t1=None, t2=None)[source]

A processor based on the physical implementation of a linear spin chain qubits system. The available Hamiltonian of the system is predefined. The processor can simulate the evolution under the given control pulses either numerically or analytically.

Parameters
N: int

The number of qubits in the system.

correct_global_phase: float

Save the global phase, the analytical solution will track the global phase. It has no effect on the numerical solution.

sx: int or list

The delta for each of the qubits in the system.

sz: int or list

The epsilon for each of the qubits in the system.

sxsy: int or list

The interaction strength for each of the qubit pair in the system.

t1: list or float, optional

Characterize the decoherence of amplitude damping for each qubit.

t2: list of float, optional

Characterize the decoherence of dephasing for each qubit.

add_control(qobj, targets=None, cyclic_permutation=False, label=None)

Add a control Hamiltonian to the processor. It creates a new Pulse object for the device that is turned off (tlist = None, coeff = None). To activate the pulse, one can set its tlist and coeff.

Parameters
qobj: :class:qutip.Qobj

The Hamiltonian for the control pulse..

targets: list, optional

The indices of the target qubits (or subquantum system of other dimensions).

cyclic_permutation: bool, optional

If true, the Hamiltonian will be expanded for all cyclic permutation of the target qubits.

label: str, optional

The label (name) of the pulse

add_drift(qobj, targets, cyclic_permutation=False)

Add a drift Hamiltonians. The drift Hamiltonians are intrinsic of the quantum system and cannot be controlled by external field.

Parameters
qobj: :class:qutip.Qobj

The drift Hamiltonian.

targets: list

The indices of the target qubits (or subquantum system of other dimensions).

add_noise(noise)

Add a noise object to the processor

Parameters
noise: :class:.Noise

The noise object defined outside the processor

add_pulse(pulse)

Add a new pulse to the device.

Parameters
pulse: :class:.Pulse

adjacent_gates(qc)[source]

Method to resolve 2 qubit gates with non-adjacent control/s or target/s in terms of gates with adjacent interactions for linear/circular spin chain system.

Parameters
qc: :class:.QubitCircuit

The circular spin chain circuit to be resolved

setup: Boolean

Linear of Circular spin chain setup

Returns
qc: QubitCircuit

Returns QubitCircuit of resolved gates for the qubit circuit in the desired basis.

property coeffs

A list of the coefficients for all control pulses.

property ctrls

A list of Hamiltonians of all pulses.

eliminate_auxillary_modes(U)

Eliminate the auxillary modes like the cavity modes in cqed. (Defined in subclasses)

get_full_coeffs(full_tlist=None)

Return the full coefficients in a 2d matrix form. Each row corresponds to one pulse. If the tlist are different for different pulses, the length of each row will be same as the full_tlist (see method get_full_tlist). Interpolation is used for adding the missing coefficient according to spline_kind.

Returns
coeffs: array-like 2d

The coefficients for all ideal pulses.

get_full_tlist(tol=1e-10)

Return the full tlist of the ideal pulses. If different pulses have different time steps, it will collect all the time steps in a sorted array.

Returns
full_tlist: array-like 1d

The full time sequence for the ideal evolution.

get_noisy_pulses(device_noise=False, drift=False)

It takes the pulses defined in the Processor and adds noise according to Processor.noise. It does not modify the pulses saved in Processor.pulses but returns a new list. The length of the new list of noisy pulses might be longer because of drift Hamiltonian and device noise. They will be added to the end of the pulses list.

Parameters
device_noise: bool, optional

If true, include pulse independent noise such as single qubit Relaxation. Default is False.

drift: bool, optional

If true, include drift Hamiltonians. Default is False.

Returns
noisy_pulses: list of Pulse

A list of noisy pulses.

get_operators_labels()[source]

Get the labels for each Hamiltonian. It is used in the methodplot_pulses. It is a 2-d nested list, in the plot, a different color will be used for each sublist.

get_ops_and_u()

Get the labels for each Hamiltonian.

Returns
ctrls: list

The list of Hamiltonians

coeffs: array_like

The transposed pulse matrix

get_qobjevo(args=None, noisy=False)

Create a qutip.QobjEvo representation of the evolution. It calls the method get_noisy_pulses and create the QobjEvo from it.

Parameters
args: dict, optional

Arguments for qutip.QobjEvo

noisy: bool, optional

If noise are included. Default is False.

Returns
qobjevo: qutip.QobjEvo

The qutip.QobjEvo representation of the unitary evolution.

c_ops: list of qutip.QobjEvo

A list of lindblad operators is also returned. if noisy==Flase, it is always an empty list.

load_circuit(qc, schedule_mode='ASAP', compiler=None)[source]

Decompose a QubitCircuit in to the control amplitude generating the corresponding evolution.

Parameters
qc: :class:.QubitCircuit

Takes the quantum circuit to be implemented.

setup: string

“linear” or “circular” for two sub-classes.

Returns
tlist: array_like

A NumPy array specifies the time of each coefficient

coeffs: array_like

A 2d NumPy array of the shape (len(ctrls), len(tlist)). Each row corresponds to the control pulse sequence for one Hamiltonian.

optimize_circuit(qc)

Take a quantum circuit/algorithm and convert it into the optimal form/basis for the desired physical system.

Parameters
qc: :class:.QubitCircuit

Takes the quantum circuit to be implemented.

Returns
qc: QubitCircuit

The circuit representation with elementary gates that can be implemented in this model.

plot_pulses(title=None, figsize=(12, 6), dpi=None, show_axis=False, rescale_pulse_coeffs=True, num_steps=1000)

Plot the ideal pulse coefficients.

Parameters
title: str, optional

Title for the plot.

figsize: tuple, optional

The size of the figure.

dpi: int, optional

The dpi of the figure.

show_axis: bool, optional

If the axis are shown.

rescale_pulse_coeffs: bool, optional

Rescale the hight of each pulses.

num_steps: int, optional

Number of time steps in the plot.

Returns
fig: matplotlib.figure.Figure

The Figure object for the plot.

ax: matplotlib.axes._subplots.AxesSubplot

The axes for the plot.

Notes

plot_pulses only works for array_like coefficients

pulse_matrix(dt=0.01)

Generates the pulse matrix for the desired physical system.

Returns
t, u, labels:

Returns the total time and label for every operation.

read_coeff(file_name, inctime=True)

Read the control amplitudes matrix and time list saved in the file by save_amp.

Parameters
file_name: string

Name of the file.

inctime: bool, optional

True if the time list in included in the first column.

Returns
tlist: array_like

The time list read from the file.

coeffs: array_like

The pulse matrix read from the file.

remove_pulse(indices=None, label=None)

Remove the control pulse with given indices.

Parameters
indices: int or list of int

The indices of the control Hamiltonians to be removed.

label: str

The label of the pulse

run(qc=None)

Calculate the propagator of the evolution by matrix exponentiation. This method won’t include noise or collpase.

Parameters
qc: :class:.QubitCircuit, optional

Takes the quantum circuit to be implemented. If not given, use the quantum circuit saved in the processor by load_circuit.

Returns
U_list: list

The propagator matrix obtained from the physical implementation.

run_analytically(init_state=None, qc=None)

Simulate the state evolution under the given qutip.QubitCircuit with matrice exponentiation. It will calculate the propagator with matrix exponentiation and return a list of qutip.Qobj. This method won’t include noise or collpase.

Parameters
qc: :class:.QubitCircuit, optional

Takes the quantum circuit to be implemented. If not given, use the quantum circuit saved in the processor by load_circuit.

init_state: :class:qutip.Qobj, optional

The initial state of the qubits in the register.

Returns
U_list: list

A list of propagators obtained for the physical implementation.

run_state(init_state=None, analytical=False, qc=None, states=None, **kwargs)

If analytical is False, use qutip.mesolve to calculate the time of the state evolution and return the result. Other arguments of mesolve can be given as keyword arguments. If analytical is True, calculate the propagator with matrix exponentiation and return a list of matrices.

Parameters
init_state: Qobj

Initial density matrix or state vector (ket).

analytical: boolean

If True, calculate the evolution with matrices exponentiation.

qc: :class:.QubitCircuit, optional

A quantum circuit. If given, it first calls the load_circuit and then calculate the evolution.

states: :class:qutip.Qobj, optional

Old API, same as init_state.

**kwargs

Keyword arguments for the qutip solver.

Returns
evo_result: qutip.Result

If analytical is False, an instance of the class qutip.Result will be returned.

If analytical is True, a list of matrices representation is returned.

save_coeff(file_name, inctime=True)

Save a file with the control amplitudes in each timeslot.

Parameters
file_name: string

Name of the file.

inctime: bool, optional

True if the time list should be included in the first column.

set_all_tlist(tlist)

Set the same tlist for all the pulses.

Parameters
tlist: array-like, optional

A list of time at which the time-dependent coefficients are applied. See Pulse for detailed information

set_up_ops(N)[source]

Generate the Hamiltonians for the spinchain model and save them in the attribute ctrls.

Parameters
N: int

The number of qubits in the system.

set_up_params(sx, sz, sxsy)[source]

Save the parameters in the attribute params and check the validity. The keys of params including “sx”, “sz”, and “sxsy”, each mapped to a list for parameters corresponding to each qubits. For coupling strength “sxsy”, list element i is the interaction between qubits i and i+1.

Parameters
sx: float or list

The coefficient of sigmax in the model

sz: flaot or list

The coefficient of sigmaz in the model

Notes

The coefficient of sxsy is defined in the submethods. All parameters will be multiplied by 2*pi for simplicity

to_array(params, N)

Transfer a parameter to an array.

class CircularSpinChain(N, correct_global_phase=True, sx=0.25, sz=1.0, sxsy=0.1, t1=None, t2=None)[source]

A processor based on the physical implementation of a circular spin chain qubits system. The available Hamiltonian of the system is predefined. The processor can simulate the evolution under the given control pulses either numerically or analytically.

Parameters
N: int

The number of qubits in the system.

correct_global_phase: float

Save the global phase, the analytical solution will track the global phase. It has no effect on the numerical solution.

sx: int or list

The delta for each of the qubits in the system.

sz: int or list

The epsilon for each of the qubits in the system.

sxsy: int or list

The interaction strength for each of the qubit pair in the system.

t1: list or float, optional

Characterize the decoherence of amplitude damping for each qubit.

t2: list of float, optional

Characterize the decoherence of dephasing for each qubit.

add_control(qobj, targets=None, cyclic_permutation=False, label=None)

Add a control Hamiltonian to the processor. It creates a new Pulse object for the device that is turned off (tlist = None, coeff = None). To activate the pulse, one can set its tlist and coeff.

Parameters
qobj: :class:qutip.Qobj

The Hamiltonian for the control pulse..

targets: list, optional

The indices of the target qubits (or subquantum system of other dimensions).

cyclic_permutation: bool, optional

If true, the Hamiltonian will be expanded for all cyclic permutation of the target qubits.

label: str, optional

The label (name) of the pulse

add_drift(qobj, targets, cyclic_permutation=False)

Add a drift Hamiltonians. The drift Hamiltonians are intrinsic of the quantum system and cannot be controlled by external field.

Parameters
qobj: :class:qutip.Qobj

The drift Hamiltonian.

targets: list

The indices of the target qubits (or subquantum system of other dimensions).

add_noise(noise)

Add a noise object to the processor

Parameters
noise: :class:.Noise

The noise object defined outside the processor

add_pulse(pulse)

Add a new pulse to the device.

Parameters
pulse: :class:.Pulse

adjacent_gates(qc)[source]

Method to resolve 2 qubit gates with non-adjacent control/s or target/s in terms of gates with adjacent interactions for linear/circular spin chain system.

Parameters
qc: :class:.QubitCircuit

The circular spin chain circuit to be resolved

setup: Boolean

Linear of Circular spin chain setup

Returns
qc: QubitCircuit

Returns QubitCircuit of resolved gates for the qubit circuit in the desired basis.

property coeffs

A list of the coefficients for all control pulses.

property ctrls

A list of Hamiltonians of all pulses.

eliminate_auxillary_modes(U)

Eliminate the auxillary modes like the cavity modes in cqed. (Defined in subclasses)

get_full_coeffs(full_tlist=None)

Return the full coefficients in a 2d matrix form. Each row corresponds to one pulse. If the tlist are different for different pulses, the length of each row will be same as the full_tlist (see method get_full_tlist). Interpolation is used for adding the missing coefficient according to spline_kind.

Returns
coeffs: array-like 2d

The coefficients for all ideal pulses.

get_full_tlist(tol=1e-10)

Return the full tlist of the ideal pulses. If different pulses have different time steps, it will collect all the time steps in a sorted array.

Returns
full_tlist: array-like 1d

The full time sequence for the ideal evolution.

get_noisy_pulses(device_noise=False, drift=False)

It takes the pulses defined in the Processor and adds noise according to Processor.noise. It does not modify the pulses saved in Processor.pulses but returns a new list. The length of the new list of noisy pulses might be longer because of drift Hamiltonian and device noise. They will be added to the end of the pulses list.

Parameters
device_noise: bool, optional

If true, include pulse independent noise such as single qubit Relaxation. Default is False.

drift: bool, optional

If true, include drift Hamiltonians. Default is False.

Returns
noisy_pulses: list of Pulse

A list of noisy pulses.

get_operators_labels()[source]

Get the labels for each Hamiltonian. It is used in the methodplot_pulses. It is a 2-d nested list, in the plot, a different color will be used for each sublist.

get_ops_and_u()

Get the labels for each Hamiltonian.

Returns
ctrls: list

The list of Hamiltonians

coeffs: array_like

The transposed pulse matrix

get_qobjevo(args=None, noisy=False)

Create a qutip.QobjEvo representation of the evolution. It calls the method get_noisy_pulses and create the QobjEvo from it.

Parameters
args: dict, optional

Arguments for qutip.QobjEvo

noisy: bool, optional

If noise are included. Default is False.

Returns
qobjevo: qutip.QobjEvo

The qutip.QobjEvo representation of the unitary evolution.

c_ops: list of qutip.QobjEvo

A list of lindblad operators is also returned. if noisy==Flase, it is always an empty list.

load_circuit(qc, schedule_mode='ASAP', compiler=None)[source]

Decompose a QubitCircuit in to the control amplitude generating the corresponding evolution.

Parameters
qc: :class:.QubitCircuit

Takes the quantum circuit to be implemented.

setup: string

“linear” or “circular” for two sub-classes.

Returns
tlist: array_like

A NumPy array specifies the time of each coefficient

coeffs: array_like

A 2d NumPy array of the shape (len(ctrls), len(tlist)). Each row corresponds to the control pulse sequence for one Hamiltonian.

optimize_circuit(qc)

Take a quantum circuit/algorithm and convert it into the optimal form/basis for the desired physical system.

Parameters
qc: :class:.QubitCircuit

Takes the quantum circuit to be implemented.

Returns
qc: QubitCircuit

The circuit representation with elementary gates that can be implemented in this model.

plot_pulses(title=None, figsize=(12, 6), dpi=None, show_axis=False, rescale_pulse_coeffs=True, num_steps=1000)

Plot the ideal pulse coefficients.

Parameters
title: str, optional

Title for the plot.

figsize: tuple, optional

The size of the figure.

dpi: int, optional

The dpi of the figure.

show_axis: bool, optional

If the axis are shown.

rescale_pulse_coeffs: bool, optional

Rescale the hight of each pulses.

num_steps: int, optional

Number of time steps in the plot.

Returns
fig: matplotlib.figure.Figure

The Figure object for the plot.

ax: matplotlib.axes._subplots.AxesSubplot

The axes for the plot.

Notes

plot_pulses only works for array_like coefficients

pulse_matrix(dt=0.01)

Generates the pulse matrix for the desired physical system.

Returns
t, u, labels:

Returns the total time and label for every operation.

read_coeff(file_name, inctime=True)

Read the control amplitudes matrix and time list saved in the file by save_amp.

Parameters
file_name: string

Name of the file.

inctime: bool, optional

True if the time list in included in the first column.

Returns
tlist: array_like

The time list read from the file.

coeffs: array_like

The pulse matrix read from the file.

remove_pulse(indices=None, label=None)

Remove the control pulse with given indices.

Parameters
indices: int or list of int

The indices of the control Hamiltonians to be removed.

label: str

The label of the pulse

run(qc=None)

Calculate the propagator of the evolution by matrix exponentiation. This method won’t include noise or collpase.

Parameters
qc: :class:.QubitCircuit, optional

Takes the quantum circuit to be implemented. If not given, use the quantum circuit saved in the processor by load_circuit.

Returns
U_list: list

The propagator matrix obtained from the physical implementation.

run_analytically(init_state=None, qc=None)

Simulate the state evolution under the given qutip.QubitCircuit with matrice exponentiation. It will calculate the propagator with matrix exponentiation and return a list of qutip.Qobj. This method won’t include noise or collpase.

Parameters
qc: :class:.QubitCircuit, optional

Takes the quantum circuit to be implemented. If not given, use the quantum circuit saved in the processor by load_circuit.

init_state: :class:qutip.Qobj, optional

The initial state of the qubits in the register.

Returns
U_list: list

A list of propagators obtained for the physical implementation.

run_state(init_state=None, analytical=False, qc=None, states=None, **kwargs)

If analytical is False, use qutip.mesolve to calculate the time of the state evolution and return the result. Other arguments of mesolve can be given as keyword arguments. If analytical is True, calculate the propagator with matrix exponentiation and return a list of matrices.

Parameters
init_state: Qobj

Initial density matrix or state vector (ket).

analytical: boolean

If True, calculate the evolution with matrices exponentiation.

qc: :class:.QubitCircuit, optional

A quantum circuit. If given, it first calls the load_circuit and then calculate the evolution.

states: :class:qutip.Qobj, optional

Old API, same as init_state.

**kwargs

Keyword arguments for the qutip solver.

Returns
evo_result: qutip.Result

If analytical is False, an instance of the class qutip.Result will be returned.

If analytical is True, a list of matrices representation is returned.

save_coeff(file_name, inctime=True)

Save a file with the control amplitudes in each timeslot.

Parameters
file_name: string

Name of the file.

inctime: bool, optional

True if the time list should be included in the first column.

set_all_tlist(tlist)

Set the same tlist for all the pulses.

Parameters
tlist: array-like, optional

A list of time at which the time-dependent coefficients are applied. See Pulse for detailed information

set_up_ops(N)[source]

Generate the Hamiltonians for the spinchain model and save them in the attribute ctrls.

Parameters
N: int

The number of qubits in the system.

set_up_params(sx, sz, sxsy)[source]

Save the parameters in the attribute params and check the validity. The keys of params including “sx”, “sz”, and “sxsy”, each mapped to a list for parameters corresponding to each qubits. For coupling strength “sxsy”, list element i is the interaction between qubits i and i+1.

Parameters
sx: float or list

The coefficient of sigmax in the model

sz: flaot or list

The coefficient of sigmaz in the model

Notes

The coefficient of sxsy is defined in the submethods. All parameters will be multiplied by 2*pi for simplicity

to_array(params, N)

Transfer a parameter to an array.

class DispersiveCavityQED(N, correct_global_phase=True, num_levels=10, deltamax=1.0, epsmax=9.5, w0=10.0, wq=None, eps=9.5, delta=0.0, g=0.01, t1=None, t2=None)[source]

The processor based on the physical implementation of a dispersive cavity QED system. The available Hamiltonian of the system is predefined. For a given pulse amplitude matrix, the processor can calculate the state evolution under the given control pulse, either analytically or numerically. (Only additional attributes are documented here, for others please refer to the parent class ModelProcessor)

Parameters
N: int

The number of qubits in the system.

correct_global_phase: float, optional

Save the global phase, the analytical solution will track the global phase. It has no effect on the numerical solution.

num_levels: int, optional

The number of energy levels in the resonator.

deltamax: int or list, optional

The coefficients of sigma-x for each of the qubits in the system.

epsmax: int or list, optional

The coefficients of sigma-z for each of the qubits in the system.

w0: int, optional

The base frequency of the resonator.

eps: int or list, optional

The epsilon for each of the qubits in the system.

delta: int or list, optional

The epsilon for each of the qubits in the system.

g: int or list, optional

The interaction strength for each of the qubit with the resonator.

t1: list or float

Characterize the decoherence of amplitude damping for each qubit. A list of size N or a float for all qubits.

t2: list of float

Characterize the decoherence of dephasing for each qubit. A list of size N or a float for all qubits.

Attributes
sx_ops: list

A list of sigmax Hamiltonians for each qubit.

sz_ops: list

A list of sigmaz Hamiltonians for each qubit.

cavityqubit_ops: list

A list of interacting Hamiltonians between cavity and each qubit.

sx_u: array_like

Pulse matrix for sigmax Hamiltonians.

sz_u: array_like

Pulse matrix for sigmaz Hamiltonians.

g_u: array_like

Pulse matrix for interacting Hamiltonians between cavity and each qubit.

wq: list of float

The frequency of the qubits calculated from eps and delta for each qubit.

Delta: list of float

The detuning with respect to w0 calculated from wq and w0 for each qubit.

add_control(qobj, targets=None, cyclic_permutation=False, label=None)

Add a control Hamiltonian to the processor. It creates a new Pulse object for the device that is turned off (tlist = None, coeff = None). To activate the pulse, one can set its tlist and coeff.

Parameters
qobj: :class:qutip.Qobj

The Hamiltonian for the control pulse..

targets: list, optional

The indices of the target qubits (or subquantum system of other dimensions).

cyclic_permutation: bool, optional

If true, the Hamiltonian will be expanded for all cyclic permutation of the target qubits.

label: str, optional

The label (name) of the pulse

add_drift(qobj, targets, cyclic_permutation=False)

Add a drift Hamiltonians. The drift Hamiltonians are intrinsic of the quantum system and cannot be controlled by external field.

Parameters
qobj: :class:qutip.Qobj

The drift Hamiltonian.

targets: list

The indices of the target qubits (or subquantum system of other dimensions).

add_noise(noise)

Add a noise object to the processor

Parameters
noise: :class:.Noise

The noise object defined outside the processor

add_pulse(pulse)

Add a new pulse to the device.

Parameters
pulse: :class:.Pulse

property coeffs

A list of the coefficients for all control pulses.

property ctrls

A list of Hamiltonians of all pulses.

eliminate_auxillary_modes(U)[source]

Eliminate the auxillary modes like the cavity modes in cqed.

get_full_coeffs(full_tlist=None)

Return the full coefficients in a 2d matrix form. Each row corresponds to one pulse. If the tlist are different for different pulses, the length of each row will be same as the full_tlist (see method get_full_tlist). Interpolation is used for adding the missing coefficient according to spline_kind.

Returns
coeffs: array-like 2d

The coefficients for all ideal pulses.

get_full_tlist(tol=1e-10)

Return the full tlist of the ideal pulses. If different pulses have different time steps, it will collect all the time steps in a sorted array.

Returns
full_tlist: array-like 1d

The full time sequence for the ideal evolution.

get_noisy_pulses(device_noise=False, drift=False)

It takes the pulses defined in the Processor and adds noise according to Processor.noise. It does not modify the pulses saved in Processor.pulses but returns a new list. The length of the new list of noisy pulses might be longer because of drift Hamiltonian and device noise. They will be added to the end of the pulses list.

Parameters
device_noise: bool, optional

If true, include pulse independent noise such as single qubit Relaxation. Default is False.

drift: bool, optional

If true, include drift Hamiltonians. Default is False.

Returns
noisy_pulses: list of Pulse

A list of noisy pulses.

get_operators_labels()[source]

Get the labels for each Hamiltonian. It is used in the methodplot_pulses. It is a 2-d nested list, in the plot, a different color will be used for each sublist.

get_ops_and_u()

Get the labels for each Hamiltonian.

Returns
ctrls: list

The list of Hamiltonians

coeffs: array_like

The transposed pulse matrix

get_qobjevo(args=None, noisy=False)

Create a qutip.QobjEvo representation of the evolution. It calls the method get_noisy_pulses and create the QobjEvo from it.

Parameters
args: dict, optional

Arguments for qutip.QobjEvo

noisy: bool, optional

If noise are included. Default is False.

Returns
qobjevo: qutip.QobjEvo

The qutip.QobjEvo representation of the unitary evolution.

c_ops: list of qutip.QobjEvo

A list of lindblad operators is also returned. if noisy==Flase, it is always an empty list.

load_circuit(qc, schedule_mode='ASAP', compiler=None)[source]

Decompose a QubitCircuit in to the control amplitude generating the corresponding evolution.

Parameters
qc: :class:.QubitCircuit

Takes the quantum circuit to be implemented.

Returns
tlist: array_like

A NumPy array specifies the time of each coefficient

coeffs: array_like

A 2d NumPy array of the shape (len(ctrls), len(tlist)). Each row corresponds to the control pulse sequence for one Hamiltonian.

optimize_circuit(qc)[source]

Take a quantum circuit/algorithm and convert it into the optimal form/basis for the desired physical system.

Parameters
qc: :class:.QubitCircuit

Takes the quantum circuit to be implemented.

Returns
qc: QubitCircuit

The circuit representation with elementary gates that can be implemented in this model.

plot_pulses(title=None, figsize=(12, 6), dpi=None, show_axis=False, rescale_pulse_coeffs=True, num_steps=1000)

Plot the ideal pulse coefficients.

Parameters
title: str, optional

Title for the plot.

figsize: tuple, optional

The size of the figure.

dpi: int, optional

The dpi of the figure.

show_axis: bool, optional

If the axis are shown.

rescale_pulse_coeffs: bool, optional

Rescale the hight of each pulses.

num_steps: int, optional

Number of time steps in the plot.

Returns
fig: matplotlib.figure.Figure

The Figure object for the plot.

ax: matplotlib.axes._subplots.AxesSubplot

The axes for the plot.

Notes

plot_pulses only works for array_like coefficients

pulse_matrix(dt=0.01)

Generates the pulse matrix for the desired physical system.

Returns
t, u, labels:

Returns the total time and label for every operation.

read_coeff(file_name, inctime=True)

Read the control amplitudes matrix and time list saved in the file by save_amp.

Parameters
file_name: string

Name of the file.

inctime: bool, optional

True if the time list in included in the first column.

Returns
tlist: array_like

The time list read from the file.

coeffs: array_like

The pulse matrix read from the file.

remove_pulse(indices=None, label=None)

Remove the control pulse with given indices.

Parameters
indices: int or list of int

The indices of the control Hamiltonians to be removed.

label: str

The label of the pulse

run(qc=None)

Calculate the propagator of the evolution by matrix exponentiation. This method won’t include noise or collpase.

Parameters
qc: :class:.QubitCircuit, optional

Takes the quantum circuit to be implemented. If not given, use the quantum circuit saved in the processor by load_circuit.

Returns
U_list: list

The propagator matrix obtained from the physical implementation.

run_analytically(init_state=None, qc=None)

Simulate the state evolution under the given qutip.QubitCircuit with matrice exponentiation. It will calculate the propagator with matrix exponentiation and return a list of qutip.Qobj. This method won’t include noise or collpase.

Parameters
qc: :class:.QubitCircuit, optional

Takes the quantum circuit to be implemented. If not given, use the quantum circuit saved in the processor by load_circuit.

init_state: :class:qutip.Qobj, optional

The initial state of the qubits in the register.

Returns
U_list: list

A list of propagators obtained for the physical implementation.

run_state(init_state=None, analytical=False, qc=None, states=None, **kwargs)

If analytical is False, use qutip.mesolve to calculate the time of the state evolution and return the result. Other arguments of mesolve can be given as keyword arguments. If analytical is True, calculate the propagator with matrix exponentiation and return a list of matrices.

Parameters
init_state: Qobj

Initial density matrix or state vector (ket).

analytical: boolean

If True, calculate the evolution with matrices exponentiation.

qc: :class:.QubitCircuit, optional

A quantum circuit. If given, it first calls the load_circuit and then calculate the evolution.

states: :class:qutip.Qobj, optional

Old API, same as init_state.

**kwargs

Keyword arguments for the qutip solver.

Returns
evo_result: qutip.Result

If analytical is False, an instance of the class qutip.Result will be returned.

If analytical is True, a list of matrices representation is returned.

save_coeff(file_name, inctime=True)

Save a file with the control amplitudes in each timeslot.

Parameters
file_name: string

Name of the file.

inctime: bool, optional

True if the time list should be included in the first column.

set_all_tlist(tlist)

Set the same tlist for all the pulses.

Parameters
tlist: array-like, optional

A list of time at which the time-dependent coefficients are applied. See Pulse for detailed information

set_up_ops(N)[source]

Generate the Hamiltonians for the spinchain model and save them in the attribute ctrls.

Parameters
N: int

The number of qubits in the system.

set_up_params(N, num_levels, deltamax, epsmax, w0, wq, eps, delta, g)[source]

Save the parameters in the attribute params and check the validity. The keys of params including “sx”, “sz”, “w0”, “eps”, “delta” and “g”, each mapped to a list for parameters corresponding to each qubits. For coupling strength “g”, list element i is the interaction between qubits i and i+1.

Parameters
N: int

The number of qubits in the system.

num_levels: int

The number of energy levels in the resonator.

deltamax: list

The coefficients of sigma-x for each of the qubits in the system.

epsmax: list

The coefficients of sigma-z for each of the qubits in the system.

wo: int

The base frequency of the resonator.

wq: list

The frequency of the qubits.

eps: list

The epsilon for each of the qubits in the system.

delta: list

The delta for each of the qubits in the system.

g: list

The interaction strength for each of the qubit with the resonator.

Notes

All parameters will be multiplied by 2*pi for simplicity

to_array(params, N)

Transfer a parameter to an array.

class Noise[source]

The base class representing noise in a processor. The noise object can be added to Processor and contributes to evolution.

get_noisy_dynamics(dims, pulses, systematic_noise)[source]

Return a pulses list added with noise and the pulse independent noise in a dummy Pulse object.

Parameters
dims: list, optional

The dimension of the components system, the default value is [2,2…,2] for qubits system.

pulses: list of :class:.Pulse

The input pulses, on which the noise object is to be applied.

systematic_noise: :class:.Pulse

The dummy pulse with no ideal control element.

Returns
noisy_pulses: list of Pulse

Noisy pulses.

systematic_noise: Pulse

The dummy pulse representing pulse independent noise.

class DecoherenceNoise(c_ops, targets=None, coeff=None, tlist=None, all_qubits=False)[source]

The decoherence noise in a processor. It generates lindblad noise according to the given collapse operator c_ops.

Parameters
c_ops: :class:qutip.Qobj or list

The Hamiltonian representing the dynamics of the noise.

targets: int or list, optional

The indices of qubits that are acted on. Default is on all qubits

coeff: list, optional

A list of the coefficients for the control Hamiltonians.

tlist: array_like, optional

A NumPy array specifies the time of each coefficient.

all_qubits: bool, optional

If c_ops contains only single qubits collapse operator, all_qubits=True will allow it to be applied to all qubits.

Attributes
c_ops: :class:qutip.Qobj or list

The Hamiltonian representing the dynamics of the noise.

targets: int or list

The indices of qubits that are acted on.

coeff: list

A list of the coefficients for the control Hamiltonians.

tlist: array_like

A NumPy array specifies the time of each coefficient.

all_qubits: bool

If c_ops contains only single qubits collapse operator, all_qubits=True will allow it to be applied to all qubits.

get_noisy_dynamics(dims=None, pulses=None, systematic_noise=None)[source]

Return a pulses list added with noise and the pulse independent noise in a dummy Pulse object.

Parameters
dims: list, optional

The dimension of the components system, the default value is [2,2…,2] for qubits system.

pulses: list of :class:.Pulse

The input pulses, on which the noise object is to be applied.

systematic_noise: :class:.Pulse

The dummy pulse with no ideal control element.

Returns
noisy_pulses: list of Pulse

Noisy pulses.

systematic_noise: Pulse

The dummy pulse representing pulse independent noise.

class RelaxationNoise(t1=None, t2=None, targets=None)[source]

The decoherence on each qubit characterized by two time scales t1 and t2.

Parameters
t1: float or list, optional

Characterize the decoherence of amplitude damping for each qubit.

t2: float or list, optional

Characterize the decoherence of dephasing for each qubit.

targets: int or list, optional

The indices of qubits that are acted on. Default is on all qubits

Attributes
t1: float or list

Characterize the decoherence of amplitude damping for each qubit.

t2: float or list

Characterize the decoherence of dephasing for each qubit.

targets: int or list

The indices of qubits that are acted on.

get_noisy_dynamics(dims=None, pulses=None, systematic_noise=None)[source]

Return a pulses list added with noise and the pulse independent noise in a dummy Pulse object.

Parameters
dims: list, optional

The dimension of the components system, the default value is [2,2…,2] for qubits system.

pulses: list of :class:.Pulse

The input pulses, on which the noise object is to be applied.

systematic_noise: :class:.Pulse

The dummy pulse with no ideal control element.

Returns
noisy_pulses: list of Pulse

Noisy pulses.

systematic_noise: Pulse

The dummy pulse representing pulse independent noise.

class ControlAmpNoise(coeff, tlist=None, indices=None)[source]

The noise in the amplitude of the control pulse.

Parameters
coeff: list

A list of the coefficients for the control Hamiltonians. For available choices, see qutip.QobjEvo.

tlist: array_like, optional

A NumPy array specifies the time of each coefficient.

indices: list of int, optional

The indices of target pulse in the list of pulses.

Attributes
———-
coeff: list

A list of the coefficients for the control Hamiltonians. For available choices, see qutip.QobjEvo.

tlist: array_like

A NumPy array specifies the time of each coefficient.

indices: list of int

The indices of target pulse in the list of pulses.

get_noisy_dynamics(dims=None, pulses=None, systematic_noise=None)[source]

Return a pulses list added with noise and the pulse independent noise in a dummy Pulse object.

Parameters
dims: list, optional

The dimension of the components system, the default value is [2,2…,2] for qubits system.

pulses: list of :class:.Pulse

The input pulses, on which the noise object is to be applied.

systematic_noise: :class:.Pulse

The dummy pulse with no ideal control element.

Returns
noisy_pulses: list of Pulse

Noisy pulses.

systematic_noise: Pulse

The dummy pulse representing pulse independent noise.

class RandomNoise(dt, rand_gen, indices=None, **kwargs)[source]

Random noise in the amplitude of the control pulse. The arguments for the random generator need to be given as key word arguments.

Parameters
dt: float, optional

The time interval between two random amplitude. The coefficients of the noise are the same within this time range.

rand_gen: numpy.random, optional

A random generator in numpy.random, it has to take a size parameter as the size of random numbers in the output array.

indices: list of int, optional

The indices of target pulse in the list of pulses.

**kwargs:

Key word arguments for the random number generator.

Examples

>>> gaussnoise = RandomNoise(             dt=0.1, rand_gen=np.random.normal, loc=mean, scale=std)

Attributes
dt: float, optional

The time interval between two random amplitude. The coefficients of the noise are the same within this time range.

rand_gen: numpy.random, optional

A random generator in numpy.random, it has to take a size parameter.

indices: list of int

The indices of target pulse in the list of pulses.

**kwargs:

Key word arguments for the random number generator.

get_noisy_dynamics(dims=None, pulses=None, systematic_noise=None)[source]

Return a pulses list added with noise and the pulse independent noise in a dummy Pulse object.

Parameters
dims: list, optional

The dimension of the components system, the default value is [2,2…,2] for qubits system.

pulses: list of :class:.Pulse

The input pulses, on which the noise object is to be applied.

systematic_noise: :class:.Pulse

The dummy pulse with no ideal control element.

Returns
noisy_pulses: list of Pulse

Noisy pulses.

systematic_noise: Pulse

The dummy pulse representing pulse independent noise.

class Pulse(qobj, targets, tlist=None, coeff=None, spline_kind=None, label='')[source]

Representation of a control pulse and the pulse dependent noise. The pulse is characterized by the ideal control pulse, the coherent noise and the lindblad noise. The later two are lists of noisy evolution dynamics. Each dynamic element is characterized by four variables: qobj, targets, tlist and coeff.

See examples for different construction behavior.

Parameters
qobj: :class:’qutip.Qobj’

The Hamiltonian of the ideal pulse.

targets: list

target qubits of the ideal pulse (or subquantum system of other dimensions).

tlist: array-like, optional

tlist of the ideal pulse. A list of time at which the time-dependent coefficients are applied. tlist does not have to be equidistant, but must have the same length or one element shorter compared to coeff. See documentation for the parameter spline_kind.

coeff: array-like or bool, optional

Time-dependent coefficients of the ideal control pulse. If an array, the length must be the same or one element longer compared to tlist. See documentation for the parameter spline_kind. If a bool, the coefficient is a constant 1 or 0.

spline_kind: str, optional

Type of the coefficient interpolation: “step_func” or “cubic”.

-“step_func”: The coefficient will be treated as a step function. E.g. tlist=[0,1,2] and coeff=[3,2], means that the coefficient is 3 in t=[0,1) and 2 in t=[2,3). It requires len(coeff)=len(tlist)-1 or len(coeff)=len(tlist), but in the second case the last element of coeff has no effect.

-“cubic”: Use cubic interpolation for the coefficient. It requires len(coeff)=len(tlist)

label: str

The label (name) of the pulse.

Examples

Create a pulse that is turned off

>>> Pulse(sigmaz(), 0)
>>> Pulse(sigmaz(), 0, None, None)


Create a time dependent pulse

>>> tlist = np.array([0., 1., 2., 4.])
>>> coeff = np.array([0.5, 1.2, 0.8])
>>> spline_kind = "step_func"
>>> Pulse(sigmaz(), 0, tlist=tlist, coeff=coeff, spline_kind="step_func")


Create a time independent pulse

>>> Pulse(sigmaz(), 0, coeff=True)


Create a constant pulse with time range

>>> Pulse(sigmaz(), 0, tlist=tlist, coeff=True)


Create an dummy Pulse (H=0)

>>> Pulse(None, None)

Attributes
ideal_pulse: :class:._EvoElement

The ideal dynamic of the control pulse.

coherent_noise: list of :class:._EvoElement

The coherent noise caused by the control pulse. Each dynamic element is still characterized by a time-dependent Hamiltonian.

lindblad_noise: list of :class:._EvoElement

The dissipative noise of the control pulse. Each dynamic element will be treated as a (time-dependent) lindblad operator in the master equation.

spline_kind: str

See parameter spline_kind.

label: str

See parameter label.

add_coherent_noise(qobj, targets, tlist=None, coeff=None)[source]

Add a new (time-dependent) Hamiltonian to the coherent noise.

Parameters
qobj: :class:’qutip.Qobj’

The Hamiltonian of the pulse.

targets: list

target qubits of the pulse (or subquantum system of other dimensions).

tlist: array-like, optional

A list of time at which the time-dependent coefficients are applied. tlist does not have to be equidistant, but must have the same length or one element shorter compared to coeff. See documentation for the parameter spline_kind of Pulse.

coeff: array-like or bool, optional

Time-dependent coefficients of the pulse noise. If an array, the length must be the same or one element longer compared to tlist. See documentation for the parameter spline_kind of Pulse. If a bool, the coefficient is a constant 1 or 0.

add_lindblad_noise(qobj, targets, tlist=None, coeff=None)[source]

Parameters
qobj: :class:’qutip.Qobj’

The collapse operator of the lindblad noise.

targets: list

target qubits of the collapse operator (or subquantum system of other dimensions).

tlist: array-like, optional

A list of time at which the time-dependent coefficients are applied. tlist does not have to be equidistant, but must have the same length or one element shorter compared to coeff. See documentation for the parameter spline_kind of Pulse.

coeff: array-like or bool, optional

Time-dependent coefficients of the pulse noise. If an array, the length must be the same or one element longer compared to tlist. See documentation for the parameter spline_kind of Pulse. If a bool, the coefficient is a constant 1 or 0.

property coeff

See parameter coeff.

get_full_tlist(tol=1e-10)[source]

Return the full tlist of the pulses and noise. It means that if different tlist are present, they will be merged to one with all time points stored in a sorted array.

Returns
full_tlist: array-like 1d

The full time sequence for the noisy evolution.

get_ideal_qobj(dims)[source]

Get the Hamiltonian of the ideal pulse.

Parameters
dims: int or list

Dimension of the system. If int, we assume it is the number of qubits in the system. If list, it is the dimension of the component systems.

Returns
qobj: qutip.Qobj

The Hamiltonian of the ideal pulse.

get_ideal_qobjevo(dims)[source]

Get a QobjEvo representation of the ideal evolution.

Parameters
dims: int or list

Dimension of the system. If int, we assume it is the number of qubits in the system. If list, it is the dimension of the component systems.

Returns
ideal_evo: qutip.QobjEvo

A QobjEvo representing the ideal evolution.

get_noisy_qobjevo(dims)[source]

Get the QobjEvo representation of the noisy evolution. The result can be used directly as input for the qutip solvers.

Parameters
dims: int or list

Dimension of the system. If int, we assume it is the number of qubits in the system. If list, it is the dimension of the component systems.

Returns
noisy_evo: qutip.QobjEvo

A QobjEvo representing the ideal evolution and coherent noise.

c_ops: list of qutip.QobjEvo

A list of (time-dependent) lindbald operators.

print_info()[source]

Print the information of the pulse, including the ideal dynamics, the coherent noise and the lindblad noise.

property qobj

See parameter qobj.

property targets

See parameter targets.

property tlist

See parameter tlist

class GateCompiler(N, params=None, pulse_dict=None)[source]

Base class. It compiles a QubitCircuit into the pulse sequence for the processor. The core member function compile calls compiling method from the sub-class and concatenate the compiled pulses.

Parameters
N: int

The number of the component systems.

params: dict, optional

A Python dictionary contains the name and the value of the parameters, such as laser frequency, detuning etc. It will be saved in the class attributes and can be used to calculate the control pulses.

pulse_dict: dict, optional

A map between the pulse label and its index in the pulse list. If given, the compiled pulse can be identified with (pulse_label, coeff), instead of (pulse_index, coeff). The number of key-value pairs should match the number of pulses in the processor. If it is empty, an integer pulse_index needs to be used in the compiling routine saved under the attributes gate_compiler.

Attributes
gate_compiler: dict

The Python dictionary in the form of {gate_name: compiler_function}. It saves the compiling routine for each gate. See sub-classes for implementation. Note that for continuous pulse, the first coeff should always be 0.

args: dict

Arguments for individual compiling routines. It adds more flexibility in customizing compiler.

compile(circuit, schedule_mode=None, args=None)[source]

Compile the the native gates into control pulse sequence. It calls each compiling method and concatenates the compiled pulses.

Parameters
circuit: :class:.QubitCircuit or list of

Gate A list of elementary gates that can be implemented in the corresponding hardware. The gate names have to be in gate_compiler.

schedule_mode: str, optional

"ASAP" for “as soon as possible” or "ALAP" for “as late as possible” or False or None for no schedule. Default is None.

args: dict, optional

A dictionary of arguments used in a specific gate compiler function.

Returns
tlist: array_like

A NumPy array specifies the time of each coefficient

coeffs: array_like

A 2d NumPy array of the shape (len(ctrls), len(tlist)). Each row corresponds to the control pulse sequence for one Hamiltonian.

globalphase_compiler(gate, args)[source]

Compiler for the GLOBALPHASE gate

class CavityQEDCompiler(N, params, pulse_dict, global_phase=0.0)[source]

Decompose a QubitCircuit into the pulse sequence for the processor.

Parameters
N: int

The number of qubits in the system.

params: dict

A Python dictionary contains the name and the value of the parameters. See DispersiveCavityQED.set_up_params for the definition.

global_phase: float, optional

Record of the global phase change and will be returned.

pulse_dict: dict, optional

A map between the pulse label and its index in the pulse list. If given, the compiled pulse can be identified with (pulse_label, coeff), instead of (pulse_index, coeff). The number of key-value pairs should match the number of pulses in the processor. If it is empty, an integer pulse_index needs to be used in the compiling routine saved under the attributes gate_compiler.

Attributes
N: int

The number of the component systems.

params: dict

A Python dictionary contains the name and the value of the parameters, such as laser frequency, detuning etc.

pulse_dict: dict

A map between the pulse label and its index in the pulse list.

gate_compiler: dict

The Python dictionary in the form of {gate_name: decompose_function}. It saves the decomposition scheme for each gate.

compile(circuit, schedule_mode=None, args=None)

Compile the the native gates into control pulse sequence. It calls each compiling method and concatenates the compiled pulses.

Parameters
circuit: :class:.QubitCircuit or list of

Gate A list of elementary gates that can be implemented in the corresponding hardware. The gate names have to be in gate_compiler.

schedule_mode: str, optional

"ASAP" for “as soon as possible” or "ALAP" for “as late as possible” or False or None for no schedule. Default is None.

args: dict, optional

A dictionary of arguments used in a specific gate compiler function.

Returns
tlist: array_like

A NumPy array specifies the time of each coefficient

coeffs: array_like

A 2d NumPy array of the shape (len(ctrls), len(tlist)). Each row corresponds to the control pulse sequence for one Hamiltonian.

globalphase_compiler(gate, args)[source]

Compiler for the GLOBALPHASE gate

iswap_compiler(gate, args)[source]

Compiler for the ISWAP gate

rx_compiler(gate, args)[source]

Compiler for the RX gate

rz_compiler(gate, args)[source]

Compiler for the RZ gate

sqrtiswap_compiler(gate, args)[source]

Compiler for the SQRTISWAP gate

Notes

This version of sqrtiswap_compiler has very low fidelity, please use iswap

class SpinChainCompiler(N, params, pulse_dict, setup='linear', global_phase=0.0)[source]

Compile a QubitCircuit into the pulse sequence for the processor.

Parameters
N: int

The number of qubits in the system.

params: dict

A Python dictionary contains the name and the value of the parameters. See SpinChain.set_up_params for the definition.

setup: string

“linear” or “circular” for two sub-classes.

global_phase: bool

Record of the global phase change and will be returned.

pulse_dict: dict, optional

A map between the pulse label and its index in the pulse list. If given, the compiled pulse can be identified with (pulse_label, coeff), instead of (pulse_index, coeff). The number of key-value pairs should match the number of pulses in the processor. If it is empty, an integer pulse_index needs to be used in the compiling routine saved under the attributes gate_compiler.

Attributes
N: int

The number of the component systems.

params: dict

A Python dictionary contains the name and the value of the parameters, such as laser frequency, detuning etc.

pulse_dict: dict

A map between the pulse label and its index in the pulse list.

gate_compiler: dict

The Python dictionary in the form of {gate_name: decompose_function}. It saves the decomposition scheme for each gate.

setup: string

“linear” or “circular” for two sub-classes.

global_phase: bool

Record of the global phase change and will be returned.

compile(circuit, schedule_mode=None, args=None)

Compile the the native gates into control pulse sequence. It calls each compiling method and concatenates the compiled pulses.

Parameters
circuit: :class:.QubitCircuit or list of

Gate A list of elementary gates that can be implemented in the corresponding hardware. The gate names have to be in gate_compiler.

schedule_mode: str, optional

"ASAP" for “as soon as possible” or "ALAP" for “as late as possible” or False or None for no schedule. Default is None.

args: dict, optional

A dictionary of arguments used in a specific gate compiler function.

Returns
tlist: array_like

A NumPy array specifies the time of each coefficient

coeffs: array_like

A 2d NumPy array of the shape (len(ctrls), len(tlist)). Each row corresponds to the control pulse sequence for one Hamiltonian.

globalphase_compiler(gate, args)[source]

Compiler for the GLOBALPHASE gate

iswap_compiler(gate, args)[source]

Compiler for the ISWAP gate

rx_compiler(gate, args)[source]

Compiler for the RX gate

rz_compiler(gate, args)[source]

Compiler for the RZ gate

sqrtiswap_compiler(gate, args)[source]

Compiler for the SQRTISWAP gate

class Scheduler(method='ALAP', constraint_functions=None)[source]

A gate (pulse) scheduler for quantum circuits (instructions). It schedules a given circuit or instructions to reduce the total execution time by parallelization. It uses heuristic methods mainly from in https://doi.org/10.1117/12.666419.

The scheduler includes two methods, “ASAP”, as soon as possible, and “ALAP”, as late as possible. The later is commonly used in quantum computation because of the finite lifetime of qubits.

The scheduler aims at pulse schedule and therefore does not consider merging gates to reduce the gates number. It assumes that the input circuit is optimized at the gate level and matches the hardware topology.

Parameters
method: str

“ASAP” for as soon as possible. “ALAP” for as late as possible.

constraint_functions: list, optional

A list of hardware constraint functions. Default includes a function qubit_contraint, i.e. one qubit cannot be used by two gates at the same time.

apply_constraint(ind1, ind2, instructions)[source]

Apply hardware constraint to check if two instructions can be executed in parallel.

Parameters
ind1, ind2: int

indices of the two instructions

instructions: list

The instruction list

commutation_rules(ind1, ind2, instructions)[source]

Determine if two gates commute, given that their used qubits overlap. Since usually the input gates are already in a universal gate sets, it uses an oversimplified condition:

If the two gates do not have the same name, they are considered as not commuting. If they are the same gate and have the same controls or targets, they are considered as commuting. E.g. CNOT 0, 1 commute with CNOT 0, 2.

schedule(circuit, gates_schedule=False, return_cycles_list=False, random_shuffle=False, repeat_num=0)[source]

Schedule a QubitCircuit, a list of Gates or a list of Instruction. For pulse schedule, the execution time for each Instruction is given in its duration attributes.

The scheduler first generates a quantum gates dependency graph, containing information about which gates have to be executed before some other gates. The graph preserves the mobility of the gates, i.e. commuting gates are not dependent on each other, even if they use the same qubits. Next, it computes the longest distance of each node to the start and end nodes. The distance for each dependency arrow is defined by the execution time of the instruction (By default, it is 1 for all gates). This is used as a priority measure in the next step. The gate with a longer distance to the end node and a shorter distance to the start node has higher priority. In the last step, it uses a list-schedule algorithm with hardware constraint and priority and returns a list of cycles for gates/instructions.

For pulse schedule, an additional step is required to compute the start time of each instruction. It adds the additional dependency caused by hardware constraint to the graph and recomputes the distance of each node to the start and end node. This distance is then converted to the start time of each instruction.

Parameters
circuit: QubitCircuit or list

For gate schedule, it should be a QubitCircuit or a list of Gate objects. For pulse schedule, it should be a list of Instruction objects, each with an attribute duration that indicates the execution time of this instruction.

gates_schedule: bool, optional

True, if only gates schedule is needed. This saves some computation that is only useful to pulse schedule. If the input circuit is a QubitCircuit, it will be assigned to True automatically. Otherwise, the default is False.

return_cycles_list: bool, optional

If True, the method returns the cycles_list, e.g. [{0, 2}, {1, 3}], which means that the first cycle contains gates0 and gates2 while the second cycle contains gates1 and gates3. It is only usefull for gates schedule.

random_shuffle: bool, optional

If the commuting gates are randomly scuffled to explore larger search space.

repeat_num: int, optional

Repeat the scheduling several times and use the best result. Used together with random_shuffle=Ture.

Returns
gate_cycle_indices or instruction_start_time: list

The cycle indices for each gate or the start time for each instruction.

Examples

>>> from qutip.qip.circuit import QubitCircuit
>>> from qutip.qip.scheduler import Scheduler
>>> circuit = QubitCircuit(7)
>>> circuit.add_gate("CZ", 5, 3)  # gate1
>>> circuit.add_gate("CZ", 4, 3)  # gate2
>>> circuit.add_gate("CZ", 2, 3)  # gate3
>>> circuit.add_gate("CZ", 6, 5)  # gate4
>>> circuit.add_gate("CZ", 2, 6)  # gate5
>>> circuit.add_gate("SWAP", [0, 2])  # gate6
>>>
>>> scheduler = Scheduler("ASAP")
>>> scheduler.schedule(circuit, gates_schedule=True)
[0, 1, 3, 2, 2, 3, 4]


The result list is the cycle indices for each gate. It means that the circuit can be executed in 5 gate cycles: [gate0, gate1, (gate3, gate4), (gate2, gate5), gate6] Notice that gate3 and gate4 commute with gate2, therefore, the order is changed to reduce the number of cycles.

class Instruction(gate, tlist=None, pulse_info=(), duration=1)[source]

The instruction that implements a quantum gate. It contains the control pulse required to implement the gate on a particular hardware model.

Parameters
gate: :class:.Gate

The quantum gate.

duration: list, optional

The execution time needed for the instruction.

tlist: array_like, optional

A list of time at which the time-dependent coefficients are applied. See Pulse for detailed information

pulse_info: list, optional

A list of tuples, each tuple corresponding to a pair of pulse label and pulse coefficient, in the format (str, array_like). This pulses will implement the desired gate.

Attributes
targets: list, optional

The target qubits.

controls: list, optional

The control qubits.

used_qubits: set

Union of the control and target qubits.

## Optimal control¶

class Optimizer(config, dyn, params=None)[source]

Base class for all control pulse optimisers. This class should not be instantiated, use its subclasses. This class implements the fidelity, gradient and interation callback functions. All subclass objects must be initialised with a

• OptimConfig instance - various configuration options

• Dynamics instance - describes the dynamics of the (quantum) system to be control optimised

Attributes
log_levelinteger

level of messaging output from the logger. Options are attributes of qutip.logging_utils, in decreasing levels of messaging, are: DEBUG_INTENSE, DEBUG_VERBOSE, DEBUG, INFO, WARN, ERROR, CRITICAL Anything WARN or above is effectively ‘quiet’ execution, assuming everything runs as expected. The default NOTSET implies that the level will be taken from the QuTiP settings file, which by default is WARN.

params: Dictionary

The key value pairs are the attribute name and value. Note: attributes are created if they do not exist already, and are overwritten if they do.

algstring

Algorithm to use in pulse optimisation. Options are:

• ‘GRAPE’ (default) - GRadient Ascent Pulse Engineering

• ‘CRAB’ - Chopped RAndom Basis

alg_paramsDictionary

Options that are specific to the pulse optim algorithm alg.

disp_conv_msgbool

Set true to display a convergence message (for scipy.optimize.minimize methods anyway)

optim_methodstring

a scipy.optimize.minimize method that will be used to optimise the pulse for minimum fidelity error

method_paramsDictionary

Options for the optim_method. Note that where there is an equivalent attribute of this instance or the termination_conditions (for example maxiter) it will override an value in these options

If set True then the method will approximate the gradient itself (if it has requirement and facility for this) This will mean that the fid_err_grad_wrapper will not get called Note it should be left False when using the Dynamics to calculate approximate gradients Note it is set True automatically when the alg is CRAB

amp_lboundfloat or list of floats

lower boundaries for the control amplitudes Can be a scalar value applied to all controls or a list of bounds for each control

amp_uboundfloat or list of floats

upper boundaries for the control amplitudes Can be a scalar value applied to all controls or a list of bounds for each control

boundsList of floats

Bounds for the parameters. If not set before the run_optimization call then the list is built automatically based on the amp_lbound and amp_ubound attributes. Setting this attribute directly allows specific bounds to be set for individual parameters. Note: Only some methods use bounds

dynamicsDynamics (subclass instance)

describes the dynamics of the (quantum) system to be control optimised (see Dynamics classes for details)

configOptimConfig instance

various configuration options (see OptimConfig for details)

termination_conditionsTerminationCondition instance

attributes determine when the optimisation will end

pulse_generatorPulseGen (subclass instance)

(can be) used to create initial pulses not used by the class, but set by pulseoptim.create_pulse_optimizer

statsStats

attributes of which give performance stats for the optimisation set to None to reduce overhead of calculating stats. Note it is (usually) shared with the Dynamics instance

dumpdump.OptimDump

Container for data dumped during the optimisation. Can be set by specifying the dumping level or set directly. Note this is mainly intended for user and a development debugging but could be used for status information during a long optimisation.

dumpingstring

The level of data dumping that will occur during the optimisation

dump_to_filebool

If set True then data will be dumped to file during the optimisation dumping will be set to SUMMARY during init_optim if dump_to_file is True and dumping not set. Default is False

dump_dirstring

Basically a link to dump.dump_dir. Exists so that it can be set through optim_params. If dump is None then will return None or will set dumping to SUMMARY when setting a path

iter_summaryOptimIterSummary

Summary of the most recent iteration. Note this is only set if dummping is on

apply_method_params(params=None)[source]

Loops through all the method_params (either passed here or the method_params attribute) If the name matches an attribute of this object or the termination conditions object, then the value of this attribute is set. Otherwise it is assumed to a method_option for the scipy.optimize.minimize function

apply_params(params=None)[source]

Set object attributes based on the dictionary (if any) passed in the instantiation, or passed as a parameter This is called during the instantiation automatically. The key value pairs are the attribute name and value Note: attributes are created if they do not exist already, and are overwritten if they do.

property dumping

The level of data dumping that will occur during the optimisation

• NONE : No processing data dumped (Default)

• SUMMARY : A summary at each iteration will be recorded

• FULL : All logs will be generated and dumped

• CUSTOM : Some customised level of dumping

When first set to CUSTOM this is equivalent to SUMMARY. It is then up to the user to specify which logs are dumped

fid_err_func_wrapper(*args)[source]

Get the fidelity error achieved using the ctrl amplitudes passed in as the first argument.

This is called by generic optimisation algorithm as the func to the minimised. The argument is the current variable values, i.e. control amplitudes, passed as a flat array. Hence these are reshaped as [nTimeslots, n_ctrls] and then used to update the stored ctrl values (if they have changed)

The error is checked against the target, and the optimisation is terminated if the target has been achieved.

fid_err_grad_wrapper(*args)[source]

Get the gradient of the fidelity error with respect to all of the variables, i.e. the ctrl amplidutes in each timeslot

This is called by generic optimisation algorithm as the gradients of func to the minimised wrt the variables. The argument is the current variable values, i.e. control amplitudes, passed as a flat array. Hence these are reshaped as [nTimeslots, n_ctrls] and then used to update the stored ctrl values (if they have changed)

Although the optimisation algorithms have a check within them for function convergence, i.e. local minima, the sum of the squares of the normalised gradient is checked explicitly, and the optimisation is terminated if this is below the min_gradient_norm condition

init_optim(term_conds)[source]

Check optimiser attribute status and passed parameters before running the optimisation. This is called by run_optimization, but could called independently to check the configuration.

iter_step_callback_func(*args)[source]

Check the elapsed wall time for the optimisation run so far. Terminate if this has exceeded the maximum allowed time

run_optimization(term_conds=None)[source]

This default function optimisation method is a wrapper to the scipy.optimize.minimize function.

It will attempt to minimise the fidelity error with respect to some parameters, which are determined by _get_optim_var_vals (see below)

The optimisation end when one of the passed termination conditions has been met, e.g. target achieved, wall time, or function call or iteration count exceeded. Note these conditions include gradient minimum met (local minima) for methods that use a gradient.

The function minimisation method is taken from the optim_method attribute. Note that not all of these methods have been tested. Note that some of these use a gradient and some do not. See the scipy documentation for details. Options specific to the method can be passed setting the method_params attribute.

If the parameter term_conds=None, then the termination_conditions attribute must already be set. It will be overwritten if the parameter is not None

The result is returned in an OptimResult object, which includes the final fidelity, time evolution, reason for termination etc

class OptimizerBFGS(config, dyn, params=None)[source]

Implements the run_optimization method using the BFGS algorithm

run_optimization(term_conds=None)[source]

Optimise the control pulse amplitudes to minimise the fidelity error using the BFGS (Broyden–Fletcher–Goldfarb–Shanno) algorithm The optimisation end when one of the passed termination conditions has been met, e.g. target achieved, gradient minimum met (local minima), wall time / iteration count exceeded.

Essentially this is wrapper to the: scipy.optimize.fmin_bfgs function

If the parameter term_conds=None, then the termination_conditions attribute must already be set. It will be overwritten if the parameter is not None

The result is returned in an OptimResult object, which includes the final fidelity, time evolution, reason for termination etc

class OptimizerLBFGSB(config, dyn, params=None)[source]

Implements the run_optimization method using the L-BFGS-B algorithm

Attributes
max_metric_corrinteger

The maximum number of variable metric corrections used to define the limited memory matrix. That is the number of previous gradient values that are used to approximate the Hessian see the scipy.optimize.fmin_l_bfgs_b documentation for description of m argument

init_optim(term_conds)[source]

Check optimiser attribute status and passed parameters before running the optimisation. This is called by run_optimization, but could called independently to check the configuration.

run_optimization(term_conds=None)[source]

Optimise the control pulse amplitudes to minimise the fidelity error using the L-BFGS-B algorithm, which is the constrained (bounded amplitude values), limited memory, version of the Broyden–Fletcher–Goldfarb–Shanno algorithm.

The optimisation end when one of the passed termination conditions has been met, e.g. target achieved, gradient minimum met (local minima), wall time / iteration count exceeded.

Essentially this is wrapper to the: scipy.optimize.fmin_l_bfgs_b function This in turn is a warpper for well established implementation of the L-BFGS-B algorithm written in Fortran, which is therefore very fast. See SciPy documentation for credit and details on this function.

If the parameter term_conds=None, then the termination_conditions attribute must already be set. It will be overwritten if the parameter is not None

The result is returned in an OptimResult object, which includes the final fidelity, time evolution, reason for termination etc

class OptimizerCrab(config, dyn, params=None)[source]

Optimises the pulse using the CRAB algorithm [1]. It uses the scipy.optimize.minimize function with the method specified by the optim_method attribute. See Optimizer.run_optimization for details It minimises the fidelity error function with respect to the CRAB basis function coefficients.

init_optim(term_conds)[source]

Check optimiser attribute status and passed parameters before running the optimisation. This is called by run_optimization, but could called independently to check the configuration.

class OptimizerCrabFmin(config, dyn, params=None)[source]

Optimises the pulse using the CRAB algorithm [1], [2]. It uses the scipy.optimize.fmin function which is effectively a wrapper for the Nelder-Mead method. It minimises the fidelity error function with respect to the CRAB basis function coefficients. This is the default Optimizer for CRAB.

References

1

P. Doria, T. Calarco & S. Montangero. Phys. Rev. Lett. 106, 190501 (2011).

2

T. Caneva, T. Calarco, & S. Montangero. Phys. Rev. A 84, 022326 (2011).

run_optimization(term_conds=None)[source]

This function optimisation method is a wrapper to the scipy.optimize.fmin function.

It will attempt to minimise the fidelity error with respect to some parameters, which are determined by _get_optim_var_vals which in the case of CRAB are the basis function coefficients

The optimisation end when one of the passed termination conditions has been met, e.g. target achieved, wall time, or function call or iteration count exceeded. Specifically to the fmin method, the optimisation will stop when change parameter values is less than xtol or the change in function value is below ftol.

If the parameter term_conds=None, then the termination_conditions attribute must already be set. It will be overwritten if the parameter is not None

The result is returned in an OptimResult object, which includes the final fidelity, time evolution, reason for termination etc

class OptimIterSummary[source]

A summary of the most recent iteration of the pulse optimisation

Attributes
iter_numint

Iteration number of the pulse optimisation

fid_func_call_numint

Fidelity function call number of the pulse optimisation

Gradient function call number of the pulse optimisation

fid_errfloat

Fidelity error

fidelity gradient (wrt the control parameters) vector norm that is the magnitude of the gradient

wall_timefloat

Time spent computing the pulse optimisation so far (in seconds of elapsed time)

class TerminationConditions[source]

Base class for all termination conditions Used to determine when to stop the optimisation algorithm Note different subclasses should be used to match the type of optimisation being used

Attributes
fid_err_targfloat

Target fidelity error

fid_goalfloat

goal fidelity, e.g. 1 - self.fid_err_targ It its typical to set this for unitary systems

max_wall_timefloat

# maximum time for optimisation (seconds)

Minimum normalised gradient after which optimisation will terminate

max_iterationsinteger

Maximum iterations of the optimisation algorithm

max_fid_func_callsinteger

Maximum number of calls to the fidelity function during the optimisation algorithm

accuracy_factorfloat

Determines the accuracy of the result. Typical values for accuracy_factor are: 1e12 for low accuracy; 1e7 for moderate accuracy; 10.0 for extremely high accuracy scipy.optimize.fmin_l_bfgs_b factr argument. Only set for specific methods (fmin_l_bfgs_b) that uses this Otherwise the same thing is passed as method_option ftol (although the scale is different) Hence it is not defined here, but may be set by the user

class OptimResult[source]

Attributes give the result of the pulse optimisation attempt

Attributes
termination_reasonstring

Description of the reason for terminating the optimisation

fidelityfloat

final (normalised) fidelity that was achieved

initial_fid_errfloat

fidelity error before optimisation starting

fid_errfloat

final fidelity error that was achieved

goal_achievedboolean

True is the fidely error achieved was below the target

Final value of the sum of the squares of the (normalised) fidelity error gradients

True if the optimisation terminated due to the minimum value of the gradient being reached

num_iterinteger

Number of iterations of the optimisation algorithm completed

max_iter_exceededboolean

True if the iteration limit was reached

max_fid_func_exceededboolean

True if the fidelity function call limit was reached

wall_timefloat

time elapsed during the optimisation

wall_time_limit_exceededboolean

True if the wall time limit was reached

timearray[num_tslots+1] of float

Time are the start of each timeslot with the final value being the total evolution time

initial_ampsarray[num_tslots, n_ctrls]

The amplitudes at the start of the optimisation

final_ampsarray[num_tslots, n_ctrls]

The amplitudes at the end of the optimisation

evo_full_finalQobj

The evolution operator from t=0 to t=T based on the final amps

evo_full_initialQobj

The evolution operator from t=0 to t=T based on the initial amps

statsStats

Object contaning the stats for the run (if any collected)

optimizerOptimizer

Instance of the Optimizer used to generate the result

class Dynamics(optimconfig, params=None)[source]

This is a base class only. See subclass descriptions and choose an appropriate one for the application.

Note that initialize_controls must be called before most of the methods can be used. init_timeslots can be called sometimes earlier in order to access timeslot related attributes

This acts as a container for the operators that are used to calculate time evolution of the system under study. That is the dynamics generators (Hamiltonians, Lindbladians etc), the propagators from one timeslot to the next, and the evolution operators. Due to the large number of matrix additions and multiplications, for small systems at least, the optimisation performance is much better using ndarrays to represent these operators. However

Attributes
log_levelinteger

level of messaging output from the logger. Options are attributes of qutip.logging_utils, in decreasing levels of messaging, are: DEBUG_INTENSE, DEBUG_VERBOSE, DEBUG, INFO, WARN, ERROR, CRITICAL Anything WARN or above is effectively ‘quiet’ execution, assuming everything runs as expected. The default NOTSET implies that the level will be taken from the QuTiP settings file, which by default is WARN

params: Dictionary

The key value pairs are the attribute name and value Note: attributes are created if they do not exist already, and are overwritten if they do.

statsStats

Attributes of which give performance stats for the optimisation set to None to reduce overhead of calculating stats. Note it is (usually) shared with the Optimizer object

tslot_computerTimeslotComputer (subclass instance)

Used to manage when the timeslot dynamics generators, propagators, gradients etc are updated

prop_computerPropagatorComputer (subclass instance)

Used to compute the propagators and their gradients

fid_computerFidelityComputer (subclass instance)

Used to computer the fidelity error and the fidelity error gradient.

memory_optimizationint

Level of memory optimisation. Setting to 0 (default) means that execution speed is prioritized over memory. Setting to 1 means that some memory prioritisation steps will be taken, for instance using Qobj (and hence sparse arrays) as the the internal operator data type, and not caching some operators Potentially further memory saving maybe made with memory_optimization > 1. The options are processed in _set_memory_optimizations, see this for more information. Individual memory saving options can be switched by settting them directly (see below)

oper_dtypetype

Data type for internal dynamics generators, propagators and time evolution operators. This can be ndarray or Qobj. Qobj may perform better for larger systems, and will also perform better when (custom) fidelity measures use Qobj methods such as partial trace. See _choose_oper_dtype for how this is chosen when not specified

cache_phased_dyn_genbool

If True then the dynamics generators will be saved with and without the propagation prefactor (if there is one) Defaults to True when memory_optimization=0, otherwise False

If the True then the propagator gradients (for exact gradients) will be computed when the propagator are computed and cache until the are used by the fidelity computer. If False then the fidelity computer will calculate them as needed. Defaults to True when memory_optimization=0, otherwise False

If True then DynamicsUnitary will cached the adjoint of the Hamiltion eignvector matrix Defaults to True when memory_optimization=0, otherwise False

sparse_eigen_decomp: bool

If True then DynamicsUnitary will use the sparse eigenvalue decomposition. Defaults to True when memory_optimization<=1, otherwise False

num_tslotsinteger

Number of timeslots (aka timeslices)

num_ctrlsinteger

calculate the of controls from the length of the control list

evo_timefloat

Total time for the evolution

tauarray[num_tslots] of float

Duration of each timeslot Note that if this is set before initialize_controls is called then num_tslots and evo_time are calculated from tau, otherwise tau is generated from num_tslots and evo_time, that is equal size time slices

timearray[num_tslots+1] of float

Cumulative time for the evolution, that is the time at the start of each time slice

drift_dyn_genQobj or list of Qobj

Drift or system dynamics generator (Hamiltonian) Matrix defining the underlying dynamics of the system Can also be a list of Qobj (length num_tslots) for time varying drift dynamics

ctrl_dyn_genList of Qobj

Control dynamics generator (Hamiltonians) List of matrices defining the control dynamics

initialQobj

Starting state / gate The matrix giving the initial state / gate, i.e. at time 0 Typically the identity for gate evolution

targetQobj

Target state / gate: The matrix giving the desired state / gate for the evolution

ctrl_ampsarray[num_tslots, num_ctrls] of float

Control amplitudes The amplitude (scale factor) for each control in each timeslot

initial_ctrl_scalingfloat

Scale factor applied to be applied the control amplitudes when they are initialised This is used by the PulseGens rather than in any fucntions in this class

initial_ctrl_offsetfloat

Linear offset applied to be applied the control amplitudes when they are initialised This is used by the PulseGens rather than in any fucntions in this class

dyn_genList of Qobj

List of combined dynamics generators (Qobj) for each timeslot

proplist of Qobj

List of propagators (Qobj) for each timeslot

prop_gradarray[num_tslots, num_ctrls] of Qobj

Array of propagator gradients (Qobj) for each timeslot, control

fwd_evoList of Qobj

List of evolution operators (Qobj) from the initial to the given

onwd_evoList of Qobj

List of evolution operators (Qobj) from the initial to the given

onto_evoList of Qobj

List of evolution operators (Qobj) from the initial to the given

evo_currentBoolean

Used to flag that the dynamics used to calculate the evolution operators is current. It is set to False when the amplitudes change

fact_mat_round_precfloat

Rounding precision used when calculating the factor matrix to determine if two eigenvalues are equivalent Only used when the PropagatorComputer uses diagonalisation

def_amps_fnamestring

Default name for the output used when save_amps is called

unitarity_check_levelint

If > 0 then unitarity of the system evolution is checked at at evolution recomputation. level 1 checks all propagators level 2 checks eigen basis as well Default is 0

unitarity_tol :

Tolerance used in checking if operator is unitary Default is 1e-10

dumpdump.DynamicsDump

Store of historical calculation data. Set to None (Default) for no storing of historical data Use dumping property to set level of data dumping

dumpingstring

The level of data dumping that will occur during the time evolution calculation.

dump_to_filebool

If set True then data will be dumped to file during the calculations dumping will be set to SUMMARY during init_evo if dump_to_file is True and dumping not set. Default is False

dump_dirstring

Basically a link to dump.dump_dir. Exists so that it can be set through dyn_params. If dump is None then will return None or will set dumping to SUMMARY when setting a path

apply_params(params=None)[source]

Set object attributes based on the dictionary (if any) passed in the instantiation, or passed as a parameter This is called during the instantiation automatically. The key value pairs are the attribute name and value Note: attributes are created if they do not exist already, and are overwritten if they do.

combine_dyn_gen(k)[source]

Computes the dynamics generator for a given timeslot The is the combined Hamiltion for unitary systems

compute_evolution()[source]

Recalculate the time evolution operators Dynamics generators (e.g. Hamiltonian) and prop (propagators) are calculated as necessary Actual work is completed by the recompute_evolution method of the timeslot computer

property dumping

The level of data dumping that will occur during the time evolution calculation.

• NONE : No processing data dumped (Default)

• SUMMARY : A summary of each time evolution will be recorded

• FULL : All operators used or created in the calculation dumped

• CUSTOM : Some customised level of dumping

When first set to CUSTOM this is equivalent to SUMMARY. It is then up to the user to specify which operators are dumped. WARNING: FULL could consume a lot of memory!

property dyn_gen

List of combined dynamics generators (Qobj) for each timeslot

property dyn_gen_phase

Some op that is applied to the dyn_gen before expontiating to get the propagator. See phase_application for how this is applied

flag_system_changed()[source]

Flag evolution, fidelity and gradients as needing recalculation

property full_evo

Full evolution - time evolution at final time slot

property fwd_evo

List of evolution operators (Qobj) from the initial to the given timeslot

get_ctrl_dyn_gen(j)[source]

Get the dynamics generator for the control Not implemented in the base class. Choose a subclass

get_drift_dim()[source]

Returns the size of the matrix that defines the drift dynamics that is assuming the drift is NxN, then this returns N

get_dyn_gen(k)[source]

Get the combined dynamics generator for the timeslot Not implemented in the base class. Choose a subclass

get_num_ctrls()[source]

calculate the of controls from the length of the control list sets the num_ctrls property, which can be used alternatively subsequently

init_timeslots()[source]

Generate the timeslot duration array ‘tau’ based on the evo_time and num_tslots attributes, unless the tau attribute is already set in which case this step in ignored Generate the cumulative time array ‘time’ based on the tau values

initialize_controls(amps, init_tslots=True)[source]

Set the initial control amplitudes and time slices Note this must be called after the configuration is complete before any dynamics can be calculated

property num_ctrls

calculate the of controls from the length of the control list sets the num_ctrls property, which can be used alternatively subsequently

property onto_evo

List of evolution operators (Qobj) from the initial to the given timeslot

property onwd_evo

List of evolution operators (Qobj) from the initial to the given timeslot

property phase_application

scalar(string), default=’preop’ Determines how the phase is applied to the dynamics generators

• ‘preop’ : P = expm(phase*dyn_gen)

• ‘postop’ : P = expm(dyn_gen*phase)

• ‘custom’ : Customised phase application

The ‘custom’ option assumes that the _apply_phase method has been set to a custom function.

Type

phase_application

property prop

List of propagators (Qobj) for each timeslot

property prop_grad

Array of propagator gradients (Qobj) for each timeslot, control

refresh_drift_attribs()[source]

Reset the dyn_shape, dyn_dims and time_depend_drift attribs

save_amps(file_name=None, times=None, amps=None, verbose=False)[source]

Save a file with the current control amplitudes in each timeslot The first column in the file will be the start time of the slot

Parameters
file_namestring

Name of the file If None given the def_amps_fname attribuite will be used

timesList type (or string)

List / array of the start times for each slot If None given this will be retrieved through get_amp_times() If ‘exclude’ then times will not be saved in the file, just the amplitudes

ampsArray[num_tslots, num_ctrls]

Amplitudes to be saved If None given the ctrl_amps attribute will be used

verboseBoolean

If True then an info message will be logged

unitarity_check()[source]

Checks whether all propagators are unitary

update_ctrl_amps(new_amps)[source]

Determine if any amplitudes have changed. If so, then mark the timeslots as needing recalculation The actual work is completed by the compare_amps method of the timeslot computer

class DynamicsGenMat(optimconfig, params=None)[source]

This sub class can be used for any system where no additional operator is applied to the dynamics generator before calculating the propagator, e.g. classical dynamics, Lindbladian

class DynamicsUnitary(optimconfig, params=None)[source]

This is the subclass to use for systems with dynamics described by unitary matrices. E.g. closed systems with Hermitian Hamiltonians Note a matrix diagonalisation is used to compute the exponent The eigen decomposition is also used to calculate the propagator gradient. The method is taken from DYNAMO (see file header)

Attributes
drift_hamQobj

This is the drift Hamiltonian for unitary dynamics It is mapped to drift_dyn_gen during initialize_controls

ctrl_hamList of Qobj

These are the control Hamiltonians for unitary dynamics It is mapped to ctrl_dyn_gen during initialize_controls

HList of Qobj

The combined drift and control Hamiltonians for each timeslot These are the dynamics generators for unitary dynamics. It is mapped to dyn_gen during initialize_controls

check_unitarity()[source]

Checks whether all propagators are unitary For propagators found not to be unitary, the potential underlying causes are investigated.

initialize_controls(amplitudes, init_tslots=True)[source]

Set the initial control amplitudes and time slices Note this must be called after the configuration is complete before any dynamics can be calculated

property num_ctrls

calculate the of controls from the length of the control list sets the num_ctrls property, which can be used alternatively subsequently

class DynamicsSymplectic(optimconfig, params=None)[source]

Symplectic systems This is the subclass to use for systems where the dynamics is described by symplectic matrices, e.g. coupled oscillators, quantum optics

Attributes
omegaarray[drift_dyn_gen.shape]

matrix used in the calculation of propagators (time evolution) with symplectic systems.

property dyn_gen_phase

The phasing operator for the symplectic group generators usually refered to as Omega By default this is applied as ‘postop’ dyn_gen*-Omega If phase_application is ‘preop’ it is applied as Omega*dyn_gen

class PropagatorComputer(dynamics, params=None)[source]

Base for all Propagator Computer classes that are used to calculate the propagators, and also the propagator gradient when exact gradient methods are used Note: they must be instantiated with a Dynamics object, that is the container for the data that the functions operate on This base class cannot be used directly. See subclass descriptions and choose the appropriate one for the application

Attributes
log_levelinteger

level of messaging output from the logger. Options are attributes of qutip_utils.logging, in decreasing levels of messaging, are: DEBUG_INTENSE, DEBUG_VERBOSE, DEBUG, INFO, WARN, ERROR, CRITICAL Anything WARN or above is effectively ‘quiet’ execution, assuming everything runs as expected. The default NOTSET implies that the level will be taken from the QuTiP settings file, which by default is WARN

indicates whether the computer class instance is capable of computing propagator gradients. It is used to determine whether to create the Dynamics prop_grad array

apply_params(params=None)[source]

Set object attributes based on the dictionary (if any) passed in the instantiation, or passed as a parameter This is called during the instantiation automatically. The key value pairs are the attribute name and value Note: attributes are created if they do not exist already, and are overwritten if they do.

reset()[source]

reset any configuration data

class PropCompApproxGrad(dynamics, params=None)[source]

This subclass can be used when the propagator is calculated simply by expm of the dynamics generator, i.e. when gradients will be calculated using approximate methods.

reset()[source]

reset any configuration data

class PropCompDiag(dynamics, params=None)[source]

Coumputes the propagator exponentiation using diagonalisation of of the dynamics generator

reset()[source]

reset any configuration data

class PropCompFrechet(dynamics, params=None)[source]

Frechet method for calculating the propagator: exponentiating the combined dynamics generator and the propagator gradient. It should work for all systems, e.g. unitary, open, symplectic. There are other PropagatorComputer subclasses that may be more efficient.

reset()[source]

reset any configuration data

class FidelityComputer(dynamics, params=None)[source]

Base class for all Fidelity Computers. This cannot be used directly. See subclass descriptions and choose one appropriate for the application Note: this must be instantiated with a Dynamics object, that is the container for the data that the methods operate on

Attributes
log_levelinteger

level of messaging output from the logger. Options are attributes of qutip.logging_utils, in decreasing levels of messaging, are: DEBUG_INTENSE, DEBUG_VERBOSE, DEBUG, INFO, WARN, ERROR, CRITICAL Anything WARN or above is effectively ‘quiet’ execution, assuming everything runs as expected. The default NOTSET implies that the level will be taken from the QuTiP settings file, which by default is WARN

dimensional_normfloat

Normalisation constant

fid_norm_funcfunction

Used to normalise the fidelity See SU and PSU options for the unitary dynamics

Used to normalise the fidelity gradient See SU and PSU options for the unitary dynamics

uses_onwd_evoboolean

flag to specify whether the onwd_evo evolution operator (see Dynamics) is used by the FidelityComputer

uses_onto_evoboolean
flag to specify whether the onto_evo evolution operator

(see Dynamics) is used by the FidelityComputer

fid_errfloat

Last computed value of the fidelity error

fidelityfloat

Last computed value of the normalised fidelity

fidelity_currentboolean

flag to specify whether the fidelity / fid_err are based on the current amplitude values. Set False when amplitudes change

Last computed values for the fidelity error gradients wrt the control in the timeslot

Last computed value for the norm of the fidelity error gradients (sqrt of the sum of the squares)

flag to specify whether the fidelity / fid_err are based on the current amplitude values. Set False when amplitudes change

apply_params(params=None)[source]

Set object attributes based on the dictionary (if any) passed in the instantiation, or passed as a parameter This is called during the instantiation automatically. The key value pairs are the attribute name and value Note: attributes are created if they do not exist already, and are overwritten if they do.

clear()[source]

clear any temporarily held status data

flag_system_changed()[source]

Flag fidelity and gradients as needing recalculation

get_fid_err()[source]

returns the absolute distance from the maximum achievable fidelity

get_fid_err_gradient()[source]

Returns the normalised gradient of the fidelity error in a (nTimeslots x n_ctrls) array wrt the timeslot control amplitude

init_comp()[source]

initialises the computer based on the configuration of the Dynamics

reset()[source]

reset any configuration data and clear any temporarily held status data

class FidCompUnitary(dynamics, params=None)[source]

Computes fidelity error and gradient assuming unitary dynamics, e.g. closed qubit systems Note fidelity and gradient calculations were taken from DYNAMO (see file header)

Attributes
phase_optionstring
determines how global phase is treated in fidelity calculations:

PSU - global phase ignored SU - global phase included

fidelity_prenormcomplex

Last computed value of the fidelity before it is normalised It is stored to use in the gradient normalisation calculation

fidelity_prenorm_currentboolean

flag to specify whether fidelity_prenorm are based on the current amplitude values. Set False when amplitudes change

clear()[source]

clear any temporarily held status data

compute_fid_grad()[source]

Calculates exact gradient of function wrt to each timeslot control amplitudes. Note these gradients are not normalised These are returned as a (nTimeslots x n_ctrls) array

flag_system_changed()[source]

Flag fidelity and gradients as needing recalculation

get_fid_err()[source]

Gets the absolute error in the fidelity

get_fid_err_gradient()[source]

Returns the normalised gradient of the fidelity error in a (nTimeslots x n_ctrls) array The gradients are cached in case they are requested mutliple times between control updates (although this is not typically found to happen)

get_fidelity()[source]

Gets the appropriately normalised fidelity value The normalisation is determined by the fid_norm_func pointer which should be set in the config

get_fidelity_prenorm()[source]

Gets the current fidelity value prior to normalisation Note the gradient function uses this value The value is cached, because it is used in the gradient calculation

init_comp()[source]

Check configuration and initialise the normalisation

init_normalization()[source]

Calc norm of <Ufinal | Ufinal> to scale subsequent norms When considering unitary time evolution operators, this basically results in calculating the trace of the identity matrix and is hence equal to the size of the target matrix There may be situations where this is not the case, and hence it is not assumed to be so. The normalisation function called should be set to either the PSU - global phase ignored SU - global phase respected

normalize_PSU(A)[source]
normalize_SU(A)[source]
normalize_gradient_PSU(grad)[source]

Normalise the gradient matrix passed as grad This PSU version is independent of global phase

normalize_gradient_SU(grad)[source]

Normalise the gradient matrix passed as grad This SU version respects global phase

reset()[source]

reset any configuration data and clear any temporarily held status data

set_phase_option(phase_option=None)[source]

Deprecated - use phase_option Phase options are SU - global phase important PSU - global phase is not important

class FidCompTraceDiff(dynamics, params=None)[source]

Computes fidelity error and gradient for general system dynamics by calculating the the fidelity error as the trace of the overlap of the difference between the target and evolution resulting from the pulses with the transpose of the same. This should provide a distance measure for dynamics described by matrices Note the gradient calculation is taken from: ‘Robust quantum gates for open systems via optimal control: Markovian versus non-Markovian dynamics’ Frederik F Floether, Pierre de Fouquieres, and Sophie G Schirmer

Attributes
scale_factorfloat

The fidelity error calculated is of some arbitary scale. This factor can be used to scale the fidelity error such that it may represent some physical measure If None is given then it is caculated as 1/2N, where N is the dimension of the drift, when the Dynamics are initialised.

compute_fid_err_grad()[source]

Calculate exact gradient of the fidelity error function wrt to each timeslot control amplitudes. Uses the trace difference norm fidelity These are returned as a (nTimeslots x n_ctrls) array

get_fid_err()[source]

Gets the absolute error in the fidelity

get_fid_err_gradient()[source]

Returns the normalised gradient of the fidelity error in a (nTimeslots x n_ctrls) array The gradients are cached in case they are requested mutliple times between control updates (although this is not typically found to happen)

init_comp()[source]

initialises the computer based on the configuration of the Dynamics Calculates the scale_factor is not already set

reset()[source]

reset any configuration data and clear any temporarily held status data

class FidCompTraceDiffApprox(dynamics, params=None)[source]

As FidCompTraceDiff, except uses the finite difference method to compute approximate gradients

Attributes
epsilonfloat

control amplitude offset to use when approximating the gradient wrt a timeslot control amplitude

compute_fid_err_grad()[source]

Calculates gradient of function wrt to each timeslot control amplitudes. Note these gradients are not normalised They are calulated These are returned as a (nTimeslots x n_ctrls) array

reset()[source]

reset any configuration data and clear any temporarily held status data

class TimeslotComputer(dynamics, params=None)[source]

Base class for all Timeslot Computers Note: this must be instantiated with a Dynamics object, that is the container for the data that the methods operate on

Attributes
log_levelinteger

level of messaging output from the logger. Options are attributes of qutip.logging_utils, in decreasing levels of messaging, are: DEBUG_INTENSE, DEBUG_VERBOSE, DEBUG, INFO, WARN, ERROR, CRITICAL Anything WARN or above is effectively ‘quiet’ execution, assuming everything runs as expected. The default NOTSET implies that the level will be taken from the QuTiP settings file, which by default is WARN

evo_comp_summaryEvoCompSummary

A summary of the most recent evolution computation Used in the stats and dump Will be set to None if neither stats or dump are set

apply_params(params=None)[source]

Set object attributes based on the dictionary (if any) passed in the instantiation, or passed as a parameter This is called during the instantiation automatically. The key value pairs are the attribute name and value Note: attributes are created if they do not exist already, and are overwritten if they do.

dump_current()[source]

Store a copy of the current time evolution

class TSlotCompUpdateAll(dynamics, params=None)[source]

Timeslot Computer - Update All Updates all dynamics generators, propagators and evolutions when ctrl amplitudes are updated

compare_amps(new_amps)[source]

Determine if any amplitudes have changed. If so, then mark the timeslots as needing recalculation Returns: True if amplitudes are the same, False if they have changed

get_timeslot_for_fidelity_calc()[source]

Returns the timeslot index that will be used calculate current fidelity value. This (default) method simply returns the last timeslot

recompute_evolution()[source]

Recalculates the evolution operators. Dynamics generators (e.g. Hamiltonian) and prop (propagators) are calculated as necessary

class PulseGen(dyn=None, params=None)[source]

Pulse generator Base class for all Pulse generators The object can optionally be instantiated with a Dynamics object, in which case the timeslots and amplitude scaling and offset are copied from that. Otherwise the class can be used independently by setting: tau (array of timeslot durations) or num_tslots and pulse_time for equally spaced timeslots

Attributes
num_tslotsinteger

Number of timeslots, aka timeslices (copied from Dynamics if given)

pulse_timefloat

total duration of the pulse (copied from Dynamics.evo_time if given)

scalingfloat

linear scaling applied to the pulse (copied from Dynamics.initial_ctrl_scaling if given)

offsetfloat

linear offset applied to the pulse (copied from Dynamics.initial_ctrl_offset if given)

tauarray[num_tslots] of float

Duration of each timeslot (copied from Dynamics if given)

lboundfloat

Lower boundary for the pulse amplitudes Note that the scaling and offset attributes can be used to fully bound the pulse for all generators except some of the random ones This bound (if set) may result in additional shifting / scaling Default is -Inf

uboundfloat

Upper boundary for the pulse amplitudes Note that the scaling and offset attributes can be used to fully bound the pulse for all generators except some of the random ones This bound (if set) may result in additional shifting / scaling Default is Inf

periodicboolean

True if the pulse generator produces periodic pulses

randomboolean

True if the pulse generator produces random pulses

log_levelinteger

level of messaging output from the logger. Options are attributes of qutip.logging_utils, in decreasing levels of messaging, are: DEBUG_INTENSE, DEBUG_VERBOSE, DEBUG, INFO, WARN, ERROR, CRITICAL Anything WARN or above is effectively ‘quiet’ execution, assuming everything runs as expected. The default NOTSET implies that the level will be taken from the QuTiP settings file, which by default is WARN

apply_params(params=None)[source]

Set object attributes based on the dictionary (if any) passed in the instantiation, or passed as a parameter This is called during the instantiation automatically. The key value pairs are the attribute name and value

gen_pulse()[source]

returns the pulse as an array of vales for each timeslot Must be implemented by subclass

init_pulse()[source]

Initialise the pulse parameters

reset()[source]

reset attributes to default values

class PulseGenRandom(dyn=None, params=None)[source]

Generates random pulses as simply random values for each timeslot

gen_pulse()[source]

Generate a pulse of random values between 1 and -1 Values are scaled using the scaling property and shifted using the offset property Returns the pulse as an array of vales for each timeslot

reset()[source]

reset attributes to default values

class PulseGenZero(dyn=None, params=None)[source]

Generates a flat pulse

gen_pulse()[source]

Generate a pulse with the same value in every timeslot. The value will be zero, unless the offset is not zero, in which case it will be the offset

class PulseGenLinear(dyn=None, params=None)[source]

Generates linear pulses

Attributes

Gradient of the line. Note this is calculated from the start_val and end_val if these are given

start_valfloat

Start point of the line. That is the starting amplitude

end_valfloat

End point of the line. That is the amplitude at the start of the last timeslot

gen_pulse(gradient=None, start_val=None, end_val=None)[source]

Generate a linear pulse using either the gradient and start value or using the end point to calulate the gradient Note that the scaling and offset parameters are still applied, so unless these values are the default 1.0 and 0.0, then the actual gradient etc will be different Returns the pulse as an array of vales for each timeslot

init_pulse(gradient=None, start_val=None, end_val=None)[source]

Calculate the gradient if pulse is defined by start and end point values

reset()[source]

reset attributes to default values

class PulseGenPeriodic(dyn=None, params=None)[source]

Intermediate class for all periodic pulse generators All of the periodic pulses range from -1 to 1 All have a start phase that can be set between 0 and 2pi

Attributes
num_wavesfloat

Number of complete waves (cycles) that occur in the pulse. wavelen and freq calculated from this if it is given

wavelenfloat

Wavelength of the pulse (assuming the speed is 1) freq is calculated from this if it is given

freqfloat

Frequency of the pulse

start_phasefloat

Phase of the pulse signal when t=0

init_pulse(num_waves=None, wavelen=None, freq=None, start_phase=None)[source]

Calculate the wavelength, frequency, number of waves etc from the each other and the other parameters If num_waves is given then the other parameters are worked from this Otherwise if the wavelength is given then it is the driver Otherwise the frequency is used to calculate wavelength and num_waves

reset()[source]

reset attributes to default values

class PulseGenSine(dyn=None, params=None)[source]

Generates sine wave pulses

gen_pulse(num_waves=None, wavelen=None, freq=None, start_phase=None)[source]

Generate a sine wave pulse If no params are provided then the class object attributes are used. If they are provided, then these will reinitialise the object attribs. returns the pulse as an array of vales for each timeslot

class PulseGenSquare(dyn=None, params=None)[source]

Generates square wave pulses

gen_pulse(num_waves=None, wavelen=None, freq=None, start_phase=None)[source]

Generate a square wave pulse If no parameters are pavided then the class object attributes are used. If they are provided, then these will reinitialise the object attribs

class PulseGenSaw(dyn=None, params=None)[source]

Generates saw tooth wave pulses

gen_pulse(num_waves=None, wavelen=None, freq=None, start_phase=None)[source]

Generate a saw tooth wave pulse If no parameters are pavided then the class object attributes are used. If they are provided, then these will reinitialise the object attribs

class PulseGenTriangle(dyn=None, params=None)[source]

Generates triangular wave pulses

gen_pulse(num_waves=None, wavelen=None, freq=None, start_phase=None)[source]

Generate a sine wave pulse If no parameters are pavided then the class object attributes are used. If they are provided, then these will reinitialise the object attribs

class PulseGenGaussian(dyn=None, params=None)[source]

Generates pulses with a Gaussian profile

gen_pulse(mean=None, variance=None)[source]

Generate a pulse with Gaussian shape. The peak is centre around the mean and the variance determines the breadth The scaling and offset attributes are applied as an amplitude and fixed linear offset. Note that the maximum amplitude will be scaling + offset.

reset()[source]

reset attributes to default values

class PulseGenGaussianEdge(dyn=None, params=None)[source]

Generate pulses with inverted Gaussian ramping in and out It’s intended use for a ramping modulation, which is often required in experimental setups.

Attributes
decay_timefloat

Determines the ramping rate. It is approximately the time required to bring the pulse to full amplitude It is set to 1/10 of the pulse time by default

gen_pulse(decay_time=None)[source]

Generate a pulse that starts and ends at zero and 1.0 in between then apply scaling and offset The tailing in and out is an inverted Gaussian shape

reset()[source]

reset attributes to default values

class PulseGenCrab(dyn=None, num_coeffs=None, params=None)[source]

Base class for all CRAB pulse generators Note these are more involved in the optimisation process as they are used to produce piecewise control amplitudes each time new optimisation parameters are tried

Attributes
num_coeffsinteger

Number of coefficients used for each basis function

num_basis_funcsinteger

Number of basis functions In this case set at 2 and should not be changed

coeffsfloat array[num_coeffs, num_basis_funcs]

The basis coefficient values

randomize_coeffsbool

If True (default) then the coefficients are set to some random values when initialised, otherwise they will all be equal to self.scaling

estimate_num_coeffs(dim)[source]

Estimate the number coefficients based on the dimensionality of the system. :returns: num_coeffs – estimated number of coefficients :rtype: int

get_optim_var_vals()[source]

Get the parameter values to be optimised :returns: :rtype: list (or 1d array) of floats

init_coeffs(num_coeffs=None)[source]

Generate the initial ceofficent values.

Parameters
num_coeffsinteger

Number of coefficients used for each basis function If given this overides the default and sets the attribute of the same name.

init_pulse(num_coeffs=None)[source]

Set the initial freq and coefficient values

reset()[source]

reset attributes to default values

set_optim_var_vals(param_vals)[source]

Set the values of the any of the pulse generation parameters based on new values from the optimisation method Typically this will be the basis coefficients

class PulseGenCrabFourier(dyn=None, num_coeffs=None, params=None)[source]

Generates a pulse using the Fourier basis functions, i.e. sin and cos

Attributes
freqsfloat array[num_coeffs]

Frequencies for the basis functions

randomize_freqsbool

If True (default) the some random offset is applied to the frequencies

gen_pulse(coeffs=None)[source]

Generate a pulse using the Fourier basis with the freqs and coeffs attributes.

Parameters
coeffsfloat array[num_coeffs, num_basis_funcs]

The basis coefficient values If given this overides the default and sets the attribute of the same name.

init_freqs()[source]

Generate the frequencies These are the Fourier harmonics with a uniformly distributed random offset

init_pulse(num_coeffs=None)[source]

Set the initial freq and coefficient values

reset()[source]

reset attributes to default values

class Stats[source]

Base class for all optimisation statistics Used for configurations where all timeslots are updated each iteration e.g. exact gradients Note that all times are generated using timeit.default_timer() and are in seconds

Attributes
dyn_gen_namestring

Text used in some report functions. Makes sense to set it to ‘Hamiltonian’ when using unitary dynamics Default is simply ‘dynamics generator’

num_iterinteger

Number of iterations of the optimisation algorithm

wall_time_optim_startfloat

Start time for the optimisation

wall_time_optim_endfloat

End time for the optimisation

wall_time_optimfloat

Time elasped during the optimisation

wall_time_dyn_gen_computefloat

Total wall (elasped) time computing combined dynamics generator (for example combining drift and control Hamiltonians)

wall_time_prop_computefloat

Total wall (elasped) time computing propagators, that is the time evolution from one timeslot to the next Includes calculating the propagator gradient for exact gradients

wall_time_fwd_prop_computefloat

Total wall (elasped) time computing combined forward propagation, that is the time evolution from the start to a specific timeslot. Excludes calculating the propagators themselves

wall_time_onwd_prop_computefloat

Total wall (elasped) time computing combined onward propagation, that is the time evolution from a specific timeslot to the end time. Excludes calculating the propagators themselves

Total wall (elasped) time computing the fidelity error gradient. Excludes calculating the propagator gradients (in exact gradient methods)

num_fidelity_func_callsinteger

Number of calls to fidelity function by the optimisation algorithm

Number of calls to gradient function by the optimisation algorithm

num_tslot_recomputeinteger

Number of time the timeslot evolution is recomputed (It is only computed if any amplitudes changed since the last call)

num_fidelity_computesinteger

Number of time the fidelity is computed (It is only computed if any amplitudes changed since the last call)

Number of time the gradient is computed (It is only computed if any amplitudes changed since the last call)

Number of times the control amplitudes are updated

Mean number of control amplitude updates per iteration

num_timeslot_changesinteger

Number of times the amplitudes of a any control in a timeslot changes

mean_num_timeslot_changes_per_updatefloat

Mean average number of timeslot amplitudes that are changed per update

num_ctrl_amp_changesinteger

Number of times individual control amplitudes that are changed

mean_num_ctrl_amp_changes_per_updatefloat

Mean average number of control amplitudes that are changed per update

calculate()[source]

Perform the calculations (e.g. averages) that are required on the stats Should be called before calling report

report()[source]

Print a report of the stats to the console

class Dump[source]

A container for dump items. The lists for dump items is depends on the type Note: abstract class

Attributes
parentsome control object (Dynamics or Optimizer)

aka the host. Object that generates the data that is dumped and is host to this dump object.

dump_dirstr

directory where files (if any) will be written out the path and be relative or absolute use ~/ to specify user home directory Note: files are only written when write_to_file is True of writeout is called explicitly Defaults to ~/.qtrl_dump

levelstring

The level of data dumping that will occur.

write_to_filebool

When set True data and summaries (as configured) will be written interactively to file during the processing Set during instantiation by the host based on its dump_to_file attrib

dump_file_extstr

Default file extension for any file names that are auto generated

fname_basestr

First part of any auto generated file names. This is usually overridden in the subclass

dump_summarybool

If True a summary is recorded each time a new item is added to the the dump. Default is True

summary_sepstr

delimiter for the summary file. default is a space

data_sepstr

delimiter for the data files (arrays saved to file). default is a space

summary_filestr

File path for summary file. Automatically generated. Can be set specifically

create_dump_dir()[source]

Checks dump directory exists, creates it if not

property level

The level of data dumping that will occur.

SUMMARY

A summary will be recorded

FULL

All possible dumping

CUSTOM

Some customised level of dumping

When first set to CUSTOM this is equivalent to SUMMARY. It is then up to the user to specify what specifically is dumped

class OptimDump(optim, level='SUMMARY')[source]

A container for dumps of optimisation data generated during the pulse optimisation.

Attributes
dump_summarybool

When True summary items are appended to the iter_summary

iter_summarylist of optimizer.OptimIterSummary

Summary at each iteration

dump_fid_errbool

When True values are appended to the fid_err_log

fid_err_loglist of float

Fidelity error at each call of the fid_err_func

When True values are appended to the fid_err_log

When True values are appended to the grad_log

add_iter_summary()[source]

add copy of current optimizer iteration summary

property dump_all

True if everything (ignoring the summary) is to be dumped

property dump_any

True if anything other than the summary is to be dumped

update_fid_err_log(fid_err)[source]

add an entry to the fid_err log

update_grad_log(grad)[source]

update_grad_norm_log(grad_norm)[source]

writeout(f=None)[source]

write all the logs and the summary out to file(s)

Parameters
ffilename or filehandle

If specified then all summary and object data will go in one file. If None is specified then type specific files will be generated in the dump_dir If a filehandle is specified then it must be a byte mode file as numpy.savetxt is used, and requires this.

class DynamicsDump(dynamics, level='SUMMARY')[source]

A container for dumps of dynamics data. Mainly time evolution calculations.

Attributes
dump_summarybool

If True a summary is recorded

evo_summarylist of tslotcomp.EvoCompSummary

Summary items are appended if dump_summary is True at each recomputation of the evolution.

dump_ampsbool

If True control amplitudes are dumped

dump_dyn_genbool

If True the dynamics generators (Hamiltonians) are dumped

dump_propbool

If True propagators are dumped

If True propagator gradients are dumped

dump_fwd_evobool

If True forward evolution operators are dumped

dump_onwd_evobool

If True onward evolution operators are dumped

dump_onto_evobool

If True onto (or backward) evolution operators are dumped

evo_dumpslist of EvoCompDumpItem

A new dump item is appended at each recomputation of the evolution. That is if any of the calculation objects are to be dumped.

add_evo_comp_summary(dump_item_idx=None)[source]

add copy of current evo comp summary

add_evo_dump()[source]

Add dump of current time evolution generating objects

property dump_all

True if all of the calculation objects are to be dumped

property dump_any

True if any of the calculation objects are to be dumped

writeout(f=None)[source]

Write all the dump items and the summary out to file(s).

Parameters
ffilename or filehandle

If specified then all summary and object data will go in one file. If None is specified then type specific files will be generated in the dump_dir. If a filehandle is specified then it must be a byte mode file as numpy.savetxt is used, and requires this.

class DumpItem[source]

An item in a dump list

class EvoCompDumpItem(dump)[source]

A copy of all objects generated to calculate one time evolution. Note the attributes are only set if the corresponding DynamicsDump dump_* attribute is set.

writeout(f=None)[source]

write all the objects out to files

Parameters
ffilename or filehandle

If specified then all object data will go in one file. If None is specified then type specific files will be generated in the dump_dir If a filehandle is specified then it must be a byte mode file as numpy.savetxt is used, and requires this.

class DumpSummaryItem`[source]

A summary of the most recent iteration. Abstract class only.

Attributes
idxint

Index in the summary list in which this is stored