Classes¶

Qobj¶

class Qobj(inpt=None, dims=[[], []], shape=[], 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:

inpt : array_like: Data for vector/matrix representation of the quantum object.
dims : list: Dimensions of object used for tensor products.
shape : list: Shape of underlying data structure (matrix shape).
copy : bool: Flag specifying whether Qobj should get a copy of the input data, or use the original.
fast : bool: Flag for fast qobj creation when running ode solvers. This parameter is used internally only.

Attributes:

data : array_like: Sparse matrix characterizing the quantum object.
dims : list: List of dimensions keeping track of the tensor structure.
shape : list: Shape of the underlying data array.
type : str: Type of quantum object: ‘bra’, ‘ket’, ‘oper’, ‘operator-ket’, ‘operator-bra’, or ‘super’.
superrep : str: Representation used if type is ‘super’. One of ‘super’ (Liouville form) or ‘choi’ (Choi matrix with tr = dimension).
isherm : bool: Indicates if quantum object represents Hermitian operator.
isunitary : bool: Indictaes if quantum object represents unitary operator.
iscp : bool: Indicates if the quantum object represents a map, and if that map is completely positive (CP).
ishp : bool: Indicates if the quantum object represents a map, and if that map is hermicity preserving (HP).
istp : bool: Indicates if the quantum object represents a map, and if that map is trace preserving (TP).
iscptp : bool: Indicates if the quantum object represents a map that is completely positive and trace preserving (CPTP).
isket : bool: Indicates if the quantum object represents a ket.
isbra : bool: Indicates if the quantum object represents a bra.
isoper : bool: Indicates if the quantum object represents an operator.
issuper : bool: Indicates if the quantum object represents a superoperator.
isoperket : bool: Indicates if the quantum object represents an operator in column vector form.
isoperbra : bool: 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.
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:	isherm : bool 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:	oper : qobj Matrix cosine of operator.
Raises:	TypeError Quantum object is not square.

Notes

Uses the Q.expm() method.

dag()[source]¶: Adjoint operator of quantum object.

diag()[source]¶

Diagonal elements of quantum object.

Returns:	diags : array 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:	B : 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:	d : float 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:

sparse : bool: Use sparse Eigensolver
sort : str: Sort eigenvalues ‘low’ to high, or ‘high’ to low.
eigvals : int: Number of requested eigenvalues. Default is all eigenvalues.
tol : float: Tolerance used by sparse Eigensolver (0=machine precision). The sparse solver may not converge if the tolerance is set too low.
maxiter : int: Maximum number of iterations performed by sparse solver (if used).

Returns:

eigvals : array: 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)[source]¶

Eigenstates and eigenenergies.

Eigenstates and eigenenergies are defined for operators and superoperators only.

Parameters:

sparse : bool: Use sparse Eigensolver
sort : str: Sort eigenvalues (and vectors) ‘low’ to high, or ‘high’ to low.
eigvals : int: Number of requested eigenvalues. Default is all eigenvalues.
tol : float: Tolerance used by sparse Eigensolver (0 = machine precision). The sparse solver may not converge if the tolerance is set too low.
maxiter : int: Maximum number of iterations performed by sparse solver (if used).

Returns:

eigvals : array: Array of eigenvalues for operator.
eigvecs : array: 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_inds : list of integer The states that should be removed. normalize : True / 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:	q : 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_list : list A nested list of Qobj instances and corresponding time-dependent coefficients. t : float The time for which to evaluate the time-dependent Qobj instance. args : dictionary A dictionary with parameter values required to evaluate the time-dependent Qobj intance.
Returns:	output : 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:	method : str {‘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:	oper : 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_inds : list of integer The states that should be kept. normalize : True / 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:	q : 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:	order : str {‘C’, ‘F’} Return array in C (default) or Fortran ordering. squeeze : bool {False, True} Squeeze output array.
Returns:	data : array 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:	sparse : bool Use sparse Eigensolver tol : float Tolerance used by sparse Eigensolver (0 = machine precision). The sparse solver may not converge if the tolerance is set too low. maxiter : int Maximum number of iterations performed by sparse solver (if used). safe : bool (default=True) Check for degenerate ground state
Returns:	eigval : float Eigenvalue for the ground state of quantum operator. eigvec : 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.

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:	bra : qobj Quantum object of type ‘bra’ or ‘ket’ ket : qobj Quantum object of type ‘ket’.
Returns:	elem : complex Complex valued matrix element.

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:

norm : str: 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’.
sparse : bool: Use sparse eigenvalue solver for trace norm. Other norms are not affected by this parameter.
tol : float: Tolerance for sparse solver (if used) for trace norm. The sparse solver may not converge if the tolerance is set too low.
maxiter : int: Maximum number of iterations performed by sparse solver (if used) for trace norm.

Returns:

norm : float: 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.

Gives the overlap (inner product) between the current bra or ket Qobj and and another bra or ket Qobj.

Parameters:	other : qobj Quantum object for a state vector of type ‘ket’ or ‘bra’.
Returns:	overlap : complex Complex valued overlap.
Raises:	TypeError Can only calculate overlap between a bra and ket 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:	order : list/array List specifying new tensor order.
Returns:	P : qobj Permuted quantum object.

proj()[source]¶

Form the projector from a given ket or bra vector.

Parameters:	Q : Qobj Input bra or ket vector
Returns:	P : Qobj Projection operator.

ptrace(sel)[source]¶

Partial trace of the quantum object.

Parameters:	sel : int/list An `int` or `list` of components to keep after partial trace.
Returns:	oper : 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.

sinm()[source]¶

Sine of a quantum operator.

Operator must be square.

Returns:	oper : 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:	sparse : bool Use sparse eigenvalue/vector solver. tol : float Tolerance used by sparse solver (0 = machine precision). maxiter : int Maximum number of iterations used by sparse solver.
Returns:	oper : 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:	atol : float Absolute tolerance used by tidyup. Default is set via qutip global settings parameters.
Returns:	oper : qobj Quantum object with small elements removed.

tr()[source]¶

Trace of a quantum object.

Returns:	trace : float Returns `real` if operator is Hermitian, returns `complex` otherwise.

trans()[source]¶

Transposed operator.

Returns:	oper : 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:	inpt : array_like A `matrix` or `list` of kets defining the transformation. inverse : bool Whether to return inverse transformation. sparse : bool Use sparse matrices when possible. Can be slower.
Returns:	oper : 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:	method : str 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:	oper : 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:	inplace : bool Do an in-place normalization norm : str Requested norm for states / operators. sparse : bool Use sparse eigensolver for trace norm. Does not affect other norms. tol : float Tolerance used by sparse eigensolver. maxiter : int Number of maximum iterations performed by sparse eigensolver.
Returns:	oper : qobj Normalized quantum object if not in-place, else None.

eseries¶

class eseries(q=array([], dtype=object), s=array([], dtype=float64))[source]¶

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

Attributes:	ampl : ndarray Array of amplitudes for exponential series. rates : ndarray Array of rates for exponential series. dims : list Dimensions of exponential series components shape : list 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:	wlist : array_like Array/list of frequenies.
Returns:	val_list : ndarray 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:	tlist : ndarray Times at which to evaluate exponential series.
Returns:	val_list : ndarray 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:

axes : instance {None}: User supplied Matplotlib axes for Bloch sphere animation.
fig : instance {None}: User supplied Matplotlib Figure instance for plotting Bloch sphere.
font_color : str {‘black’}: Color of font used for Bloch sphere labels.
font_size : int {20}: Size of font used for Bloch sphere labels.
frame_alpha : float {0.1}: Sets transparency of Bloch sphere frame.
frame_color : str {‘gray’}: Color of sphere wireframe.
frame_width : int {1}: Width of wireframe.
point_color : list {[“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_marker : list {[“o”,”s”,”d”,”^”]}: List of point marker shapes to cycle through.
point_size : list {[25,32,35,45]}: List of point marker sizes. Note, not all point markers look the same size when plotted!
sphere_alpha : float {0.2}: Transparency of Bloch sphere itself.
sphere_color : str {‘#FFDDDD’}: Color of Bloch sphere.
figsize : list {[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_color : list {[“g”,”#CC6600”,”b”,”r”]}: List of vector colors to cycle through.
vector_width : int {5}: Width of displayed vectors.
vector_style : str {‘-|>’, ‘simple’, ‘fancy’, ‘’}: Vector arrowhead style (from matplotlib’s arrow style).
vector_mutation : int {20}: Width of vectors arrowhead.
view : list {[-60,30]}: Azimuthal and Elevation viewing angles.
xlabel : list {[“$x$”,”“]}: List of strings corresponding to +x and -x axes labels, respectively.
xlpos : list {[1.1,-1.1]}: Positions of +x and -x labels respectively.
ylabel : list {[“$y$”,”“]}: List of strings corresponding to +y and -y axes labels, respectively.
ylpos : list {[1.2,-1.2]}: Positions of +y and -y labels respectively.
zlabel : list {[r’$\left|0\right>$’,r’$\left|1\right>$’]}: List of strings corresponding to +z and -z axes labels, respectively.
zlpos : list {[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_vector : Qobj/array/list/tuple: Position for the annotaion. Qobj of a qubit or a vector of 3 elements.
text : str/unicode: 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:	points : array/list Collection of data points. meth : str {‘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:	state : qobj Input state vector. kind : str {‘vector’,’point’} Type of object to plot.

add_vectors(vectors)[source]¶

Add a list of vectors to Bloch sphere.

Parameters:	vectors : array_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(fig=None, axes=None)[source]¶: Render the Bloch sphere and its data sets in on given figure and axes.

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

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

Parameters:	name : str 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. format : str Format of output image. dirc : str Directory for output images. Defaults to current working directory.
Returns:	File containing plot of Bloch sphere.

set_label_convention(convention)[source]¶

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

Parameters:	convention : string One of the following: “original” “xyz” “sx sy sz” “01” “polarization jones” “polarization jones letters” see also: http://en.wikipedia.org/wiki/Jones_calculus “polarization stokes” see also: http://en.wikipedia.org/wiki/Stokes_parameters

show()[source]¶: Display Bloch sphere and corresponding data sets.

vector_mutation = None¶: Sets the width of the vectors arrowhead

vector_style = None¶: Style of Bloch vectors, default = ‘-|>’ (or ‘simple’)

vector_width = None¶: Width of Bloch vectors, default = 5

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:	a : float Lower bound of the interval. b : float Upper bound of the interval. y : ndarray Function values at interval points. alpha : float Second-order derivative at a. Default is 0. beta : float 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:	a : float Lower bound of the interval. b : float Upper bound of the interval. coeffs : ndarray 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_sys : Qobj: System Hamiltonian
coup_op : Qobj: Operator describing the coupling between system and bath.
coup_strength : float: Coupling strength.
temperature : float: Bath temperature, in units corresponding to planck
N_cut : int: Cutoff parameter for the bath
N_exp : int: Number of exponential terms used to approximate the bath correlation functions
planck : float: reduced Planck constant
boltzmann : float: Boltzmann’s constant
options : qutip.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.
stats : qutip.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_coeff : list of complex: Coefficients for the exponential series terms
exp_freq : list 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:

options : qutip.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_freq : float Bath spectral density cutoff frequency. renorm : bool Apply renormalisation to coupling terms Can be useful if using SI units for planck and boltzmann bnd_cut_approx : bool 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:	rho0 : Qobj Initial state (density matrix) of the system. tlist : list Time over which system evolves.
Returns:	results : `qutip.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_S : qutip.Qobj: System Hamiltonian (can also be a Liouvillian)
L1 : qutip.Qobj / list of qutip.Qobj: System operators coupling into the feedback loop. Can be a single operator or a list of operators.
L2 : qutip.Qobj / list of qutip.Qobj: 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 : qutip.Qobj / list of qutip.Qobj: Decay operators describing conventional Markovian decay channels. Can be a single operator or a list of operators.
integrator : str {‘propagator’, ‘mesolve’}: Integrator method to use. Defaults to ‘propagator’ which tends to be faster for long times (i.e., large Hilbert space).
parallel : bool: Run integrator in parallel if True. Only implemented for ‘propagator’ as the integrator method.
options : qutip.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:

rho0 : qutip.Qobj: initial density matrix or state vector (ket).
blist : array_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
tlist : array_like: list of corresponding times t1,..,tn at which to evaluate the field operators
tau : float: time-delay
c1 : qutip.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)
c2 : qutip.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:

blist : array_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
tlist : array_like: list of corresponding times t1,..,tn at which to evaluate the field operators
tau : float: time-delay
c1 : qutip.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)
c2 : qutip.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)
notrace : bool {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 computing field correlation function

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

Compute propagator for time t and time-delay tau

Parameters:

t : float: current time
tau : float: time-delay
notrace : bool {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:	rho0 : `qutip.Qobj` initial density matrix or state vector (ket) t : float current time tau : float time-delay
Returns:	: :class:`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:

dynmaps : list of qutip.Qobj: List of precomputed dynamical maps (superoperators), or a callback function that returns the superoperator at a given time.
times : array_like: List of times $t_n$ at which to calculate $\rho(t_n)$
learningtimes : array_like: List of times $t_k$ to use as learning times if argument dynmaps is a callback function.
thres : float: Threshold for halting. Halts if $||T_{n}-T_{n-1}||$ is below treshold.
options : qutip.solver.Options: Generic solver options.

Solver Options and Results¶

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_steps=5, rhs_reuse=False, rhs_filename=None, ntraj=500, gui=False, rhs_with_state=False, store_final_state=False, store_states=False, seeds=None, steady_state_average=False, 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:

atol : float {1e-8}: Absolute tolerance.
rtol : float {1e-6}: Relative tolerance.
method : str {‘adams’,’bdf’}: Integration method.
order : int {12}: Order of integrator (<=12 ‘adams’, <=5 ‘bdf’)
nsteps : int {2500}: Max. number of internal steps/call.
first_step : float {0}: Size of initial step (0 = automatic).
min_step : float {0}: Minimum step size (0 = automatic).
max_step : float {0}: Maximum step size (0 = automatic)
tidy : bool {True,False}: Tidyup Hamiltonian and initial state by removing small terms.
num_cpus : int: Number of cpus used by mcsolver (default = # of cpus).
norm_tol : float: Tolerance used when finding wavefunction norm in mcsolve.
norm_steps : int: Max. number of steps used to find wavefunction norm to within norm_tol in mcsolve.
average_states : bool {False}: Average states values over trajectories in stochastic solvers.
average_expect : bool {True}: Average expectation values over trajectories for stochastic solvers.
mc_corr_eps : float {1e-10}: Arbitrarily small value for eliminating any divide-by-zero errors in correlation calculations when using mcsolve.
ntraj : int {500}: Number of trajectories in stochastic solvers.
openmp_threads : int: Number of OPENMP threads to use. Default is number of cpu cores.
rhs_reuse : bool {False,True}: Reuse Hamiltonian data.
rhs_with_state : bool {False,True}: Whether or not to include the state in the Hamiltonian function callback signature.
rhs_filename : str: Name for compiled Cython file.
seeds : ndarray: Array containing random number seeds for mcsolver.
store_final_state : bool {False, True}: Whether or not to store the final state of the evolution in the result class.
store_states : bool {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_openmp : bool {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:

solver : str: Which solver was used [e.g., ‘mesolve’, ‘mcsolve’, ‘brmesolve’, …]
times : list/array: Times at which simulation data was collected.
expect : list/array: Expectation values (if requested) for simulation.
states : array: State of the simulation (density matrix or ket) evaluated at times.
num_expect : int: Number of expectation value operators in simulation.
num_collapse : int: Number of collapse operators in simualation.
ntraj : int/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_times : list: Times at which state collpase occurred. Only for Monte Carlo solver.
col_which : list: Which collapse operator was responsible for each collapse in col_times. Only for Monte Carlo solver.

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_names : list 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:	sections : OrderedDict of _StatsSection These are the sections that are created automatically on instantiation or added using add_section header : string Some text that will be used as the heading in the report By default there is None total_time : float Time in seconds for the solver to complete processing Can be None, meaning that total timing percentages will be reported

Methods

`add_section`(name)	Add another section with the given name
`add_count`(key, value[, section])	Add value to count.
`add_timing`(key, value[, section])	Add value to timing.
`add_message`(key, value[, section, sep])	Add value to message.

report:

Output the statistics report to console or file.

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:	key : string key for the section.counts dictionary reusing a key will result in numerical addition of value value : int Initial value of the count, or added to an existing count section: string or `class` : _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:

key : string: key for the section.messages dictionary reusing a key will result in concatenation of value
value : int: Initial value of the message, or added to an existing message
sep : string: 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:	name : string will be used as key for sections dict will also be the header for the section
Returns:	section : class 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:	key : string key for the section.timings dictionary reusing a key will result in numerical addition of value value : int 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:	output : stream 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:	value : float Time in seconds to complete the solver section section : string or class Section which to set the total_time for If None given, the total_time for complete solve is set

class StochasticSolverOptions(H=None, state0=None, times=None, c_ops=[], sc_ops=[], e_ops=[], m_ops=None, args=None, ntraj=1, nsubsteps=1, d1=None, d2=None, d2_len=1, dW_factors=None, rhs=None, generate_A_ops=None, generate_noise=None, homogeneous=True, solver=None, method=None, distribution='normal', store_measurement=False, noise=None, normalize=True, options=None, progress_bar=None, map_func=None, map_kwargs=None)[source]¶

Class of options for stochastic solvers such as qutip.stochastic.ssesolve, qutip.stochastic.smesolve, etc. Options can be specified either as arguments to the constructor:

sso = StochasticSolverOptions(nsubsteps=100, ...)

or by changing the class attributes after creation:

sso = StochasticSolverOptions()
sso.nsubsteps = 1000

The stochastic solvers qutip.stochastic.ssesolve, qutip.stochastic.smesolve, qutip.stochastic.ssepdpsolve and qutip.stochastic.smepdpsolve 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.

Attributes:

H : qutip.Qobj: System Hamiltonian.
state0 : qutip.Qobj: Initial state vector (ket) or density matrix.
times : list / array: List of times for $t$. Must be uniformly spaced.
c_ops : list of qutip.Qobj: List of deterministic collapse operators.
sc_ops : list of qutip.Qobj: 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.
e_ops : list of qutip.Qobj: Single operator or list of operators for which to evaluate expectation values.
m_ops : list 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.
args : dict / list: List of dictionary of additional problem-specific parameters. Implicit methods can adjust tolerance via args = {‘tol’:value}
ntraj : int: Number of trajectors.
nsubsteps : int: Number of sub steps between each time-spep given in times.
d1 : function: Function for calculating the operator-valued coefficient to the deterministic increment dt.
d2 : function: Function for calculating the operator-valued coefficient to the stochastic increment(s) dW_n, where n is in [0, d2_len[.
d2_len : int (default 1): The number of stochastic increments in the process.
dW_factors : array: Array of length d2_len, containing scaling factors for each measurement operator in m_ops.
rhs : function: Function for calculating the deterministic and stochastic contributions to the right-hand side of the stochastic differential equation. This only needs to be specified when implementing a custom SDE solver.
generate_A_ops : function: Function that generates a list of pre-computed operators or super- operators. These precomputed operators are used in some d1 and d2 functions.
generate_noise : function: Function for generate an array of pre-computed noise signal.
homogeneous : bool (True): Wheter or not the stochastic process is homogenous. Inhomogenous processes are only supported for poisson distributions.
solver : string: Name of the solver method to use for solving the stochastic equations. Valid values are: 1/2 order algorithms: ‘euler-maruyama’, ‘fast-euler-maruyama’, ‘pc-euler’ is a predictor-corrector method which is more stable than explicit methods, 1 order algorithms: ‘milstein’, ‘fast-milstein’, ‘platen’, ‘milstein-imp’ is semi-implicit Milstein method, 3/2 order algorithms: ‘taylor15’, ‘taylor15-imp’ is semi-implicit Taylor 1.5 method. Implicit methods can adjust tolerance via args = {‘tol’:value}, default is {‘tol’:1e-6}
method : string (‘homodyne’, ‘heterodyne’, ‘photocurrent’): The name of the type of measurement process that give rise to the stochastic equation to solve. Specifying a method with this keyword argument is a short-hand notation for using pre-defined d1 and d2 functions for the corresponding stochastic processes.
distribution : string (‘normal’, ‘poission’): The name of the distribution used for the stochastic increments.
store_measurements : bool (default False): Whether or not to store the measurement results in the qutip.solver.SolverResult instance returned by the solver.
noise : array: Vector specifying the noise.
normalize : bool (default True): Whether or not to normalize the wave function during the evolution.
options : qutip.solver.Options: Generic solver options.
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_bar : qutip.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.

hamiltonian: :class: qutip.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

Attributes:

N: int

The number of two-level systems.

hamiltonian: :class: qutip.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:	lindbladian: :class: qutip.Qobj The Lindbladian matrix as a qutip.Qobj.

liouvillian()[source]¶

Build the total Liouvillian using the Dicke basis.

Returns:	liouv: :class: qutip.Qobj The Liouvillian matrix for the system.

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

Solve for diagonal Hamiltonians and initial states faster.

Parameters:	initial_state: :class: qutip.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 options: :class: qutip.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.

prune_eigenstates(liouvillian)[source]¶

Remove spurious eigenvalues and eigenvectors of the Liouvillian.

Spurious means that the given eigenvector has elements outside of the block-diagonal matrix.

Parameters:	liouvillian_eigenstates: list A list with the eigenvalues and eigenvectors of the Liouvillian including spurious ones.
Returns:	correct_eigenstates: list The list with the correct eigenvalues and eigenvectors of the Liouvillian.

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_col : int 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_col : int 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.

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:	data : array_like Data for the distribution. The dimensions must match the lengths of the coordinate arrays in xvecs. xvecs : list List of arrays that spans the space for each coordinate. xlabels : list 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:	dim : int The dimension (coordinate index) along which to obtain the marginal distribution.
Returns:	d : Distributions 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:	dim : int The dimension (coordinate index) along which to obtain the projected distribution.
Returns:	d : Distributions 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:

fig : matplotlib Figure instance: If given, use this figure instance for the visualization,
ax : matplotlib Axes instance: If given, render the visualization using this axis instance.
figsize : tuple: 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.
style : string: Type of visualization: ‘colormap’ (default) or ‘surface’.

Returns:	fig, ax : tuple 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(name, targets=None, controls=None, arg_value=None, arg_label=None)[source]¶: Representation of a quantum gate, with its required parametrs, and target and control qubits.

class QubitCircuit(N, input_states=None, output_states=None, reverse_states=True)[source]¶

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

add_1q_gate(name, start=0, end=None, qubits=None, arg_value=None, arg_label=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:	name : String Gate name. start : Integer Starting location of qubits. end : Integer Last qubit for the gate. qubits : List Specific qubits for applying gates. arg_value : Float Argument value(phi). arg_label : String 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:	qc : QubitCircuit The circuit block to be added to the main circuit. start : Integer The qubit on which the first gate is applied.

add_gate(gate, targets=None, controls=None, arg_value=None, arg_label=None)[source]¶

Adds a gate with specified parameters to the circuit.

Parameters:	gate: String or `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.

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:	qc : QubitCircuit Returns QubitCircuit of the gates for the qubit circuit with the resolved non-adjacent gates.

propagators()[source]¶

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

Returns:	U_list : list Returns list of unitary matrices for the qubit circuit.

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

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

Parameters:	index : Integer Location of gate to be removed. name : String Gate name to be removed. remove : String If first or all gate 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.

Parameters:	basis : list. Basis of the resolved circuit.
Returns:	qc : QubitCircuit Returns QubitCircuit of resolved gates for the qubit circuit in the desired basis.

reverse_circuit()[source]¶

Reverses an entire circuit of unitary gates.

Returns:	qc : QubitCircuit Returns QubitCircuit of resolved gates for the qubit circuit in the reverse order.

class CircuitProcessor(N, correct_global_phase)[source]¶

Base class for representation of the physical implementation of a quantum program/algorithm on a specified qubit system.

adjacent_gates(qc, setup)[source]¶

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

Parameters:	qc: QubitCircuit Takes the quantum circuit to be implemented. setup: String Takes the nature of the spin chain; linear or circular.
Returns:	qc: QubitCircuit The resolved circuit representation.

get_ops_and_u()[source]¶: Returns the Hamiltonian operators and corresponding values by stacking them together.

get_ops_labels()[source]¶: Returns the Hamiltonian operators and corresponding labels by stacking them together.

load_circuit(qc)[source]¶

Translates an abstract quantum circuit to its corresponding Hamiltonian for a specific model.

Parameters:	qc: QubitCircuit Takes the quantum circuit to be implemented.

optimize_circuit(qc)[source]¶

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

Parameters:	qc: QubitCircuit Takes the quantum circuit to be implemented.
Returns:	qc: QubitCircuit The optimal circuit representation.

plot_pulses()[source]¶

Maps the physical interaction between the circuit components for the desired physical system.

Returns:	fig, ax: Figure Maps the physical interaction between the circuit components.

pulse_matrix()[source]¶

Generates the pulse matrix for the desired physical system.

Returns:	t, u, labels: Returns the total time and label for every operation.

run(qc=None)[source]¶

Generates the propagator matrix by running the Hamiltonian for the appropriate time duration for the desired physical system.

Parameters:	qc: QubitCircuit Takes the quantum circuit to be implemented.
Returns:	U_list: list The propagator matrix obtained from the physical implementation.

run_state(qc=None, states=None)[source]¶

Generates the propagator matrix by running the Hamiltonian for the appropriate time duration for the desired physical system with the given initial state of the qubit register.

Parameters:	qc: QubitCircuit Takes the quantum circuit to be implemented. states: Qobj Initial state of the qubits in the register.
Returns:	U_list: list The propagator matrix obtained from the physical implementation.

class SpinChain(N, correct_global_phase=True, sx=None, sz=None, sxsy=None)[source]¶

Representation of the physical implementation of a quantum program/algorithm on a spin chain qubit system.

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: 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.

get_ops_and_u()[source]¶: Returns the Hamiltonian operators and corresponding values by stacking them together.

load_circuit(qc)[source]¶

Translates an abstract quantum circuit to its corresponding Hamiltonian for a specific model.

Parameters:	qc: QubitCircuit Takes the quantum circuit to be implemented.

class LinearSpinChain(N, correct_global_phase=True, sx=None, sz=None, sxsy=None)[source]¶

Representation of the physical implementation of a quantum program/algorithm on a spin chain qubit system arranged in a linear formation. It is a sub-class of SpinChain.

get_ops_labels()[source]¶: Returns the Hamiltonian operators and corresponding labels by stacking them together.

optimize_circuit(qc)[source]¶

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

Parameters:	qc: QubitCircuit Takes the quantum circuit to be implemented.
Returns:	qc: QubitCircuit The optimal circuit representation.

class CircularSpinChain(N, correct_global_phase=True, sx=None, sz=None, sxsy=None)[source]¶

Representation of the physical implementation of a quantum program/algorithm on a spin chain qubit system arranged in a circular formation. It is a sub-class of SpinChain.

get_ops_labels()[source]¶: Returns the Hamiltonian operators and corresponding labels by stacking them together.

optimize_circuit(qc)[source]¶

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

Parameters:	qc: QubitCircuit Takes the quantum circuit to be implemented.
Returns:	qc: QubitCircuit The optimal circuit representation.

class DispersivecQED(N, correct_global_phase=True, Nres=None, deltamax=None, epsmax=None, w0=None, wq=None, eps=None, delta=None, g=None)[source]¶

Representation of the physical implementation of a quantum program/algorithm on a dispersive cavity-QED system.

dispersive_gate_correction(qc1, rwa=True)[source]¶

Method to resolve ISWAP and SQRTISWAP gates in a cQED system by adding single qubit gates to get the correct output matrix.

Parameters:	qc: Qobj The circular spin chain circuit to be resolved rwa: Boolean Specify if RWA is used or not.
Returns:	qc: QubitCircuit Returns QubitCircuit of resolved gates for the qubit circuit in the desired basis.

get_ops_and_u()[source]¶: Returns the Hamiltonian operators and corresponding values by stacking them together.

get_ops_labels()[source]¶: Returns the Hamiltonian operators and corresponding labels by stacking them together.

load_circuit(qc)[source]¶

Translates an abstract quantum circuit to its corresponding Hamiltonian for a specific model.

Parameters:	qc: QubitCircuit Takes the quantum circuit to be implemented.

optimize_circuit(qc)[source]¶

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

Parameters:	qc: QubitCircuit Takes the quantum circuit to be implemented.
Returns:	qc: QubitCircuit The optimal circuit representation.

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_level : integer: 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.
alg : string: Algorithm to use in pulse optimisation. Options are:

‘GRAPE’ (default) - GRadient Ascent Pulse Engineering ‘CRAB’ - Chopped RAndom Basis
alg_params : Dictionary: options that are specific to the pulse optim algorithm that is GRAPE or CRAB
disp_conv_msg : bool: Set true to display a convergence message (for scipy.optimize.minimize methods anyway)
optim_method : string: a scipy.optimize.minimize method that will be used to optimise the pulse for minimum fidelity error
method_params : Dictionary: 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
approx_grad : bool: 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_lbound : float 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_ubound : float 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
bounds : List 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
dynamics : Dynamics (subclass instance): describes the dynamics of the (quantum) system to be control optimised (see Dynamics classes for details)
config : OptimConfig instance: various configuration options (see OptimConfig for details)
termination_conditions : TerminationCondition instance: attributes determine when the optimisation will end
pulse_generator : PulseGen (subclass instance): (can be) used to create initial pulses not used by the class, but set by pulseoptim.create_pulse_optimizer
stats : Stats: 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
dump : dump.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.
dumping : string: 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.
dump_to_file : bool: 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_dir : string: 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_summary : OptimIterSummary: 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.

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_corr : integer 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.

AJGP ToDo: Add citation here

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.

Notes

[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_num : int: Iteration number of the pulse optimisation
fid_func_call_num : int: Fidelity function call number of the pulse optimisation
grad_func_call_num : int: Gradient function call number of the pulse optimisation
fid_err : float: Fidelity error
grad_norm : float: fidelity gradient (wrt the control parameters) vector norm that is the magnitude of the gradient
wall_time : float: 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_targ : float: Target fidelity error
fid_goal : float: goal fidelity, e.g. 1 - self.fid_err_targ It its typical to set this for unitary systems
max_wall_time : float: # maximum time for optimisation (seconds)
min_gradient_norm : float: Minimum normalised gradient after which optimisation will terminate
max_iterations : integer: Maximum iterations of the optimisation algorithm
max_fid_func_calls : integer: Maximum number of calls to the fidelity function during the optimisation algorithm
accuracy_factor : float: 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_reason : string: Description of the reason for terminating the optimisation
fidelity : float: final (normalised) fidelity that was achieved
initial_fid_err : float: fidelity error before optimisation starting
fid_err : float: final fidelity error that was achieved
goal_achieved : boolean: True is the fidely error achieved was below the target
grad_norm_final : float: Final value of the sum of the squares of the (normalised) fidelity error gradients
grad_norm_min_reached : float: True if the optimisation terminated due to the minimum value of the gradient being reached
num_iter : integer: Number of iterations of the optimisation algorithm completed
max_iter_exceeded : boolean: True if the iteration limit was reached
max_fid_func_exceeded : boolean: True if the fidelity function call limit was reached
wall_time : float: time elapsed during the optimisation
wall_time_limit_exceeded : boolean: True if the wall time limit was reached
time : array[num_tslots+1] of float: Time are the start of each timeslot with the final value being the total evolution time
initial_amps : array[num_tslots, n_ctrls]: The amplitudes at the start of the optimisation
final_amps : array[num_tslots, n_ctrls]: The amplitudes at the end of the optimisation
evo_full_final : Qobj: The evolution operator from t=0 to t=T based on the final amps
evo_full_initial : Qobj: The evolution operator from t=0 to t=T based on the initial amps
stats : Stats: Object contaning the stats for the run (if any collected)
optimizer : Optimizer: 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_level : integer: 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.
stats : Stats: 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_computer : TimeslotComputer (subclass instance): Used to manage when the timeslot dynamics generators, propagators, gradients etc are updated
prop_computer : PropagatorComputer (subclass instance): Used to compute the propagators and their gradients
fid_computer : FidelityComputer (subclass instance): Used to computer the fidelity error and the fidelity error gradient.
memory_optimization : int: 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_dtype : type: Data type for internal dynamics generators, propagators and time evolution operators. This can be ndarray or Qobj, or (in theory) any other representaion that supports typical matrix methods (e.g. dot) ndarray performs best for smaller quantum systems. 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_gen : bool: 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
cache_prop_grad : bool: 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
cache_dyn_gen_eigenvectors_adj: bool: 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_tslots : integer: Number of timeslots (aka timeslices)
num_ctrls : integer: calculate the of controls from the length of the control list
evo_time : float: Total time for the evolution
tau : array[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
time : array[num_tslots+1] of float: Cumulative time for the evolution, that is the time at the start of each time slice
drift_dyn_gen : Qobj 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_gen : List of Qobj: Control dynamics generator (Hamiltonians) List of matrices defining the control dynamics
initial : Qobj: Starting state / gate The matrix giving the initial state / gate, i.e. at time 0 Typically the identity for gate evolution
target : Qobj: Target state / gate: The matrix giving the desired state / gate for the evolution
ctrl_amps : array[num_tslots, num_ctrls] of float: Control amplitudes The amplitude (scale factor) for each control in each timeslot
initial_ctrl_scaling : float: 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_offset : float: 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_gen : List of Qobj: List of combined dynamics generators (Qobj) for each timeslot
prop : list of Qobj: List of propagators (Qobj) for each timeslot
prop_grad : array[num_tslots, num_ctrls] of Qobj: Array of propagator gradients (Qobj) for each timeslot, control
fwd_evo : List of Qobj: List of evolution operators (Qobj) from the initial to the given
onwd_evo : List of Qobj: List of evolution operators (Qobj) from the initial to the given
onto_evo : List of Qobj: List of evolution operators (Qobj) from the initial to the given
evo_current : Boolean: 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_prec : float: Rounding precision used when calculating the factor matrix to determine if two eigenvalues are equivalent Only used when the PropagatorComputer uses diagonalisation
def_amps_fname : string: Default name for the output used when save_amps is called
unitarity_check_level : int: 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
dump : dump.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
dumping : string: The level of data dumping that will occur during the time evolution calculation.
dump_to_file : bool: 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_dir : string: 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

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!

dyn_gen¶: List of combined dynamics generators (Qobj) for each timeslot

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

full_evo¶: Full evolution - time evolution at final time slot

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

num_ctrls¶: calculate the of controls from the length of the control list sets the num_ctrls property, which can be used alternatively subsequently

onto_evo¶: List of evolution operators (Qobj) from the initial to the given timeslot

onwd_evo¶: List of evolution operators (Qobj) from the initial to the given timeslot

phase_application¶

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

prop¶: List of propagators (Qobj) for each timeslot

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_name : string: Name of the file If None given the def_amps_fname attribuite will be used
times : List 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
amps : Array[num_tslots, num_ctrls]: Amplitudes to be saved If None given the ctrl_amps attribute will be used
verbose : Boolean: 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_ham : Qobj: This is the drift Hamiltonian for unitary dynamics It is mapped to drift_dyn_gen during initialize_controls
ctrl_ham : List of Qobj: These are the control Hamiltonians for unitary dynamics It is mapped to ctrl_dyn_gen during initialize_controls
H : List 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

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:	omega : array[drift_dyn_gen.shape] matrix used in the calculation of propagators (time evolution) with symplectic systems.

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_level : integer: 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
grad_exact : boolean: 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_level : integer

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_norm : float

Normalisation constant

fid_norm_func : function

Used to normalise the fidelity See SU and PSU options for the unitary dynamics

grad_norm_func : function

Used to normalise the fidelity gradient See SU and PSU options for the unitary dynamics

uses_onwd_evo : boolean

flag to specify whether the onwd_evo evolution operator (see Dynamics) is used by the FidelityComputer

uses_onto_evo : boolean

flag to specify whether the onto_evo evolution operator: (see Dynamics) is used by the FidelityComputer

fid_err : float

Last computed value of the fidelity error

fidelity : float

Last computed value of the normalised fidelity

fidelity_current : boolean

flag to specify whether the fidelity / fid_err are based on the current amplitude values. Set False when amplitudes change

fid_err_grad: array[num_tslot, num_ctrls] of float

Last computed values for the fidelity error gradients wrt the control in the timeslot

grad_norm : float

Last computed value for the norm of the fidelity error gradients (sqrt of the sum of the squares)

fid_err_grad_current : boolean

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_option : string

determines how global phase is treated in fidelity calculations:: PSU - global phase ignored SU - global phase included

fidelity_prenorm : complex

Last computed value of the fidelity before it is normalised It is stored to use in the gradient normalisation calculation

fidelity_prenorm_current : boolean

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_factor : float 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:	epsilon : float 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_level : integer: 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_summary : EvoCompSummary: 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_tslots : integer: Number of timeslots, aka timeslices (copied from Dynamics if given)
pulse_time : float: total duration of the pulse (copied from Dynamics.evo_time if given)
scaling : float: linear scaling applied to the pulse (copied from Dynamics.initial_ctrl_scaling if given)
offset : float: linear offset applied to the pulse (copied from Dynamics.initial_ctrl_offset if given)
tau : array[num_tslots] of float: Duration of each timeslot (copied from Dynamics if given)
lbound : float: 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
ubound : float: 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
periodic : boolean: True if the pulse generator produces periodic pulses
random : boolean: True if the pulse generator produces random pulses
log_level : integer: 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 : float Gradient of the line. Note this is calculated from the start_val and end_val if these are given start_val : float Start point of the line. That is the starting amplitude end_val : float 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_waves : float Number of complete waves (cycles) that occur in the pulse. wavelen and freq calculated from this if it is given wavelen : float Wavelength of the pulse (assuming the speed is 1) freq is calculated from this if it is given freq : float Frequency of the pulse start_phase : float 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_time : float 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_coeffs : integer: Number of coefficients used for each basis function
num_basis_funcs : integer: Number of basis functions In this case set at 2 and should not be changed
coeffs : float array[num_coeffs, num_basis_funcs]: The basis coefficient values
randomize_coeffs : bool: 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_coeffs : integer 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:	freqs : float array[num_coeffs] Frequencies for the basis functions randomize_freqs : bool 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:	coeffs : float 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_name : string: Text used in some report functions. Makes sense to set it to ‘Hamiltonian’ when using unitary dynamics Default is simply ‘dynamics generator’
num_iter : integer: Number of iterations of the optimisation algorithm
wall_time_optim_start : float: Start time for the optimisation
wall_time_optim_end : float: End time for the optimisation
wall_time_optim : float: Time elasped during the optimisation
wall_time_dyn_gen_compute : float: Total wall (elasped) time computing combined dynamics generator (for example combining drift and control Hamiltonians)
wall_time_prop_compute : float: 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_compute : float: 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_compute : float: 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
wall_time_gradient_compute : float: Total wall (elasped) time computing the fidelity error gradient. Excludes calculating the propagator gradients (in exact gradient methods)
num_fidelity_func_calls : integer: Number of calls to fidelity function by the optimisation algorithm
num_grad_func_calls : integer: Number of calls to gradient function by the optimisation algorithm
num_tslot_recompute : integer: Number of time the timeslot evolution is recomputed (It is only computed if any amplitudes changed since the last call)
num_fidelity_computes : integer: Number of time the fidelity is computed (It is only computed if any amplitudes changed since the last call)
num_grad_computes : integer: Number of time the gradient is computed (It is only computed if any amplitudes changed since the last call)
num_ctrl_amp_updates : integer: Number of times the control amplitudes are updated
mean_num_ctrl_amp_updates_per_iter : float: Mean number of control amplitude updates per iteration
num_timeslot_changes : integer: Number of times the amplitudes of a any control in a timeslot changes
mean_num_timeslot_changes_per_update : float: Mean average number of timeslot amplitudes that are changed per update
num_ctrl_amp_changes : integer: Number of times individual control amplitudes that are changed
mean_num_ctrl_amp_changes_per_update : float: 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:

parent : some control object (Dynamics or Optimizer): aka the host. Object that generates the data that is dumped and is host to this dump object.
dump_dir : str: 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
level : string: 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.
write_to_file : bool: 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_ext : str: Default file extension for any file names that are auto generated
fname_base : str: First part of any auto generated file names. This is usually overridden in the subclass
dump_summary : bool: If True a summary is recorded each time a new item is added to the the dump. Default is True
summary_sep : str: delimiter for the summary file. default is a space
data_sep : str: delimiter for the data files (arrays saved to file). default is a space
summary_file : str: File path for summary file. Automatically generated. Can be set specifically

create_dump_dir()[source]¶: Checks dump directory exists, creates it if not

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_summary : bool: When True summary items are appended to the iter_summary
iter_summary : list of optimizer.OptimIterSummary: Summary at each iteration
dump_fid_err : bool: When True values are appended to the fid_err_log
fid_err_log : list of float: Fidelity error at each call of the fid_err_func
dump_grad_norm : bool: When True values are appended to the fid_err_log
grad_norm_log : list of float: Gradient norm at each call of the grad_norm_log
dump_grad : bool: When True values are appended to the grad_log
grad_log : list of ndarray: Gradients at each call of the fid_grad_func

add_iter_summary()[source]¶: add copy of current optimizer iteration summary

dump_all¶: True if everything (ignoring the summary) is to be dumped

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]¶: add an entry to the grad log

update_grad_norm_log(grad_norm)[source]¶: add an entry to the grad_norm log

writeout(f=None)[source]¶

write all the logs and the summary out to file(s)

Parameters:	f : filename 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_summary : bool: If True a summary is recorded
evo_summary : list of :class:`tslotcomp.EvoCompSummary’: Summary items are appended if dump_summary is True at each recomputation of the evolution.
dump_amps : bool: If True control amplitudes are dumped
dump_dyn_gen : bool: If True the dynamics generators (Hamiltonians) are dumped
dump_prop : bool: If True propagators are dumped
dump_prop_grad : bool: If True propagator gradients are dumped
dump_fwd_evo : bool: If True forward evolution operators are dumped
dump_onwd_evo : bool: If True onward evolution operators are dumped
dump_onto_evo : bool: If True onto (or backward) evolution operators are dumped
evo_dumps : list 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

dump_all¶: True if all of the calculation objects are to be dumped

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) :param f: 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:	f : filename 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: idx : int

Index in the summary list in which this is stored