# Source code for qutip.qip.device.spinchain

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import numpy as np
from qutip.operators import sigmax, sigmay, sigmaz, identity
from qutip.tensor import tensor
from qutip.qip.circuit import QubitCircuit
from qutip.qip.device.processor import Processor
from qutip.qip.device.modelprocessor import ModelProcessor
from qutip.qip.pulse import Pulse
from qutip.qip.compiler.gatecompiler import GateCompiler
from qutip.qip.compiler.spinchaincompiler import SpinChainCompiler

__all__ = ['SpinChain', 'LinearSpinChain', 'CircularSpinChain']

[docs]class SpinChain(ModelProcessor):
"""
The processor based on the physical implementation of
a spin chain qubits system.
The available Hamiltonian of the system is predefined.
The processor can simulate the evolution under the given
control pulses either numerically or analytically.
It is a base class and should not be used directly, please
refer the the subclasses :class:qutip.qip.LinearSpinChain and
:class:qutip.qip.CircularSpinChain.
refer to the parent class :class:qutip.qip.device.ModelProcessor)

Parameters
----------
N: int
The number of qubits in the system.

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

sx: int or list
The delta for each of the qubits in the system.

sz: int or list
The epsilon for each of the qubits in the system.

sxsy: int or list
The interaction strength for each of the qubit pair in the system.

t1: list or float
Characterize the decoherence of amplitude damping for
each qubit. A list of size N or a float for all qubits.

t2: list of float
Characterize the decoherence of dephasing for
each qubit. A list of size N or a float for all qubits.

Attributes
----------
sx: list
The delta for each of the qubits in the system.

sz: list
The epsilon for each of the qubits in the system.

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

sx_ops: list
A list of sigmax Hamiltonians for each qubit.

sz_ops: list
A list of sigmaz Hamiltonians for each qubit.

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

sx_u: array_like
Pulse matrix for sigmax Hamiltonians.

sz_u: array_like
Pulse matrix for sigmaz Hamiltonians.

sxsy_u: array_like
Pulse matrix for tensor(sigmax, sigmay) interacting Hamiltonians.
"""
def __init__(self, N, correct_global_phase,
sx, sz, sxsy, t1, t2):
super(SpinChain, self).__init__(
N, correct_global_phase=correct_global_phase, t1=t1, t2=t2)
self.correct_global_phase = correct_global_phase
self.spline_kind = "step_func"
# params and ops are set in the submethods

[docs]    def set_up_ops(self, N):
"""
Generate the Hamiltonians for the spinchain model and save them in the
attribute ctrls.

Parameters
----------
N: int
The number of qubits in the system.
"""
# sx_ops
for m in range(N):
self.pulses.append(
Pulse(sigmax(), m, spline_kind=self.spline_kind))
# sz_ops
for m in range(N):
self.pulses.append(
Pulse(sigmaz(), m, spline_kind=self.spline_kind))
# sxsy_ops
operator = tensor([sigmax(), sigmax()]) + tensor([sigmay(), sigmay()])
for n in range(N - 1):
self.pulses.append(
Pulse(operator, [n, n+1], spline_kind=self.spline_kind))

[docs]    def set_up_params(self, sx, sz):
"""
Save the parameters in the attribute params and check the validity.

Parameters
----------
sx: float or list
The coefficient of sigmax in the model

sz: flaot or list
The coefficient of sigmaz in the model

Notes
-----
The coefficient of sxsy is defined in the submethods.
All parameters will be multiplied by 2*pi for simplicity
"""
sx_para = super(SpinChain, self)._para_list(sx, self.N)
self._paras["sx"] = sx_para
sz_para = super(SpinChain, self)._para_list(sz, self.N)
self._paras["sz"] = sz_para

@property
def sx_ops(self):
return self.ctrls[: self.N]

@property
def sz_ops(self):
return self.ctrls[self.N: 2*self.N]

@property
def sxsy_ops(self):
return self.ctrls[2*self.N:]

@property
def sx_u(self):
return self.coeffs[: self.N]

@property
def sz_u(self):
return self.coeffs[self.N: 2*self.N]

@property
def sxsy_u(self):
return self.coeffs[2*self.N:]

"""
Decompose a :class:qutip.QubitCircuit in to the control
amplitude generating the corresponding evolution.

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

setup: string
"linear" or "circular" for two sub-calsses.

Returns
-------
tlist: array_like
A NumPy array specifies the time of each coefficient

coeffs: array_like
A 2d NumPy array of the shape (len(ctrls), len(tlist)). Each
row corresponds to the control pulse sequence for
one Hamiltonian.
"""
gates = self.optimize_circuit(qc).gates

dec = SpinChainCompiler(
self.N, self._paras, setup=setup,
global_phase=0., num_ops=len(self.ctrls))
tlist, self.coeffs, self.global_phase = dec.decompose(gates)
for i in range(len(self.pulses)):
self.pulses[i].tlist = tlist

return tlist, self.coeffs

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

Parameters
----------
qc: :class:qutip.QubitCircuit
The circular spin chain circuit to be resolved

setup: Boolean
Linear of Circular spin chain setup

Returns
-------
qc: :class:qutip.QubitCircuit
Returns QubitCircuit of resolved gates for the qubit circuit in the
desired basis.
"""
# FIXME This huge block has been here for a long time.
# It could be moved to the new compiler section and carefully
# splitted into smaller peaces.
qc_t = QubitCircuit(qc.N, qc.reverse_states)
swap_gates = ["SWAP", "ISWAP", "SQRTISWAP", "SQRTSWAP", "BERKELEY",
"SWAPalpha"]
N = qc.N

for gate in qc.gates:
if gate.name == "CNOT" or gate.name == "CSIGN":
start = min([gate.targets[0], gate.controls[0]])
end = max([gate.targets[0], gate.controls[0]])

if (setup == "linear" or
(setup == "circular" and (end - start) <= N // 2)):
i = start
while i < end:
if (start + end - i - i == 1 and
(end - start + 1) % 2 == 0):
# Apply required gate if control and target are
# adjacent to each other, provided |control-target|
# is even.
if end == gate.controls[0]:
controls=[i + 1])
else:
controls=[i])

elif (start + end - i - i == 2 and
(end - start + 1) % 2 == 1):
# Apply a swap between i and its adjacent gate,
# then the required gate if and then another swap
# if control and target have one qubit between
# them, provided |control-target| is odd.
if end == gate.controls[0]:
controls=[i + 2])
else:
controls=[i + 1])
i += 1

else:
# Swap the target/s and/or control with their
# adjacent qubit to bring them closer.
qc_t.add_gate("SWAP", [start + end - i - 1,
start + end - i])
i += 1

elif (end - start) < N - 1:
"""
If the resolving has to go backwards, the path is first
mapped to a separate circuit and then copied back to the
original circuit.
"""

temp = QubitCircuit(N - end + start)
i = 0
while i < (N - end + start):

if (N + start - end - i - i == 1 and
(N - end + start + 1) % 2 == 0):
if end == gate.controls[0]:
controls=[i + 1])
else:
controls=[i])

elif (N + start - end - i - i == 2 and
(N - end + start + 1) % 2 == 1):
if end == gate.controls[0]:
controls=[i + 1])
else:
controls=[i + 2])
i += 1

else:
[N + start - end - i - 1,
N + start - end - i])
i += 1

j = 0
for gate in temp.gates:
if (j < N - end - 2):
if gate.name in ["CNOT", "CSIGN"]:
end + gate.controls[0])
else:
[end + gate.targets[0],
end + gate.targets[1]])
elif (j == N - end - 2):
if gate.name in ["CNOT", "CSIGN"]:
(end + gate.controls[0]) % N)
else:
[end + gate.targets[0],
(end + gate.targets[1]) % N])
else:
if gate.name in ["CNOT", "CSIGN"]:
(end + gate.targets[0]) % N,
(end + gate.controls[0]) % N)
else:
[(end + gate.targets[0]) % N,
(end + gate.targets[1]) % N])
j = j + 1

elif (end - start) == N - 1:

elif gate.name in swap_gates:
start = min([gate.targets[0], gate.targets[1]])
end = max([gate.targets[0], gate.targets[1]])

if (setup == "linear" or
(setup == "circular" and (end - start) <= N // 2)):
i = start
while i < end:
if (start + end - i - i == 1 and
(end - start + 1) % 2 == 0):
elif ((start + end - i - i) == 2 and
(end - start + 1) % 2 == 1):
qc_t.add_gate(gate.name, [i + 1, i + 2])
i += 1
else:
qc_t.add_gate("SWAP", [start + end - i - 1,
start + end - i])
i += 1

else:
temp = QubitCircuit(N - end + start)
i = 0
while i < (N - end + start):

if (N + start - end - i - i == 1 and
(N - end + start + 1) % 2 == 0):

elif (N + start - end - i - i == 2 and
(N - end + start + 1) % 2 == 1):
temp.add_gate(gate.name, [i + 1, i + 2])
i += 1

else:
temp.add_gate("SWAP", [N + start - end - i - 1,
N + start - end - i])
i += 1

j = 0
for gate in temp.gates:
if(j < N - end - 2):
end + gate.targets[1]])
elif(j == N - end - 2):
[end + gate.targets[0],
(end + gate.targets[1]) % N])
else:
[(end + gate.targets[0]) % N,
(end + gate.targets[1]) % N])
j = j + 1

else:
gate.arg_value, gate.arg_label)

return qc_t

[docs]    def eliminate_auxillary_modes(self, U):
return U

[docs]    def optimize_circuit(self, qc):
"""
Take a quantum circuit/algorithm and convert it into the
optimal form/basis for the desired physical system.

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

Returns
-------
qc: :class:qutip.QubitCircuit
The circuit representation with elementary gates
that can be implemented in this model.
"""
self.qc0 = qc
self.qc2 = self.qc1.resolve_gates(
basis=["SQRTISWAP", "ISWAP", "RX", "RZ"])
return self.qc2

[docs]class LinearSpinChain(SpinChain):
"""
A processor based on the physical implementation of
a linear spin chain qubits system.
The available Hamiltonian of the system is predefined.
The processor can simulate the evolution under the given
control pulses either numerically or analytically.

Parameters
----------
N: int
The number of qubits in the system.

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

sx: int or list
The delta for each of the qubits in the system.

sz: int or list
The epsilon for each of the qubits in the system.

sxsy: int or list
The interaction strength for each of the qubit pair in the system.

t1: list or float, optional
Characterize the decoherence of amplitude damping for
each qubit.

t2: list of float, optional
Characterize the decoherence of dephasing for
each qubit.
"""
def __init__(self, N, correct_global_phase=True,
sx=0.25, sz=1.0, sxsy=0.1, t1=None, t2=None):

super(LinearSpinChain, self).__init__(
N, correct_global_phase=correct_global_phase,
sx=sx, sz=sz, sxsy=sxsy, t1=t1, t2=t2)
self.set_up_params(sx=sx, sz=sz, sxsy=sxsy)
self.set_up_ops(N)

[docs]    def set_up_ops(self, N):
super(LinearSpinChain, self).set_up_ops(N)

[docs]    def set_up_params(self, sx, sz, sxsy):
# Doc same as in the parent class
super(LinearSpinChain, self).set_up_params(sx, sz)
sxsy_para = self._para_list(sxsy, self.N-1)
self._paras["sxsy"] = sxsy_para

@property
def sxsy_ops(self):
return self.ctrls[2*self.N: 3*self.N-1]

@property
def sxsy_u(self):
return self.coeffs[2*self.N: 3*self.N-1]

def get_ops_labels(self):
return ([r"$\sigma_x^%d$" % n for n in range(self.N)] +
[r"$\sigma_z^%d$" % n for n in range(self.N)] +
[r"$\sigma_x^%d\sigma_x^{%d} + \sigma_y^%d\sigma_y^{%d}$"
% (n, n, n + 1, n + 1) for n in range(self.N - 1)])

[docs]class CircularSpinChain(SpinChain):
"""
A processor based on the physical implementation of
a circular spin chain qubits system.
The available Hamiltonian of the system is predefined.
The processor can simulate the evolution under the given
control pulses either numerically or analytically.

Parameters
----------
N: int
The number of qubits in the system.

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

sx: int or list
The delta for each of the qubits in the system.

sz: int or list
The epsilon for each of the qubits in the system.

sxsy: int or list
The interaction strength for each of the qubit pair in the system.

t1: list or float, optional
Characterize the decoherence of amplitude damping for
each qubit.

t2: list of float, optional
Characterize the decoherence of dephasing for
each qubit.
"""
def __init__(self, N, correct_global_phase=True,
sx=0.25, sz=1.0, sxsy=0.1, t1=None, t2=None):

super(CircularSpinChain, self).__init__(
N, correct_global_phase=correct_global_phase,
sx=sx, sz=sz, sxsy=sxsy, t1=t1, t2=t2)
self.set_up_params(sx=sx, sz=sz, sxsy=sxsy)
self.set_up_ops(N)

[docs]    def set_up_ops(self, N):
super(CircularSpinChain, self).set_up_ops(N)
operator = tensor([sigmax(), sigmax()]) + tensor([sigmay(), sigmay()])
self.pulses.append(
Pulse(operator, [N-1, 0], spline_kind=self.spline_kind))

[docs]    def set_up_params(self, sx, sz, sxsy):
# Doc same as in the parent class
super(CircularSpinChain, self).set_up_params(sx, sz)
sxsy_para = self._para_list(sxsy, self.N)
self._paras["sxsy"] = sxsy_para

@property
def sxsy_ops(self):
return self.ctrls[2*self.N: 3*self.N]

@property
def sxsy_u(self):
return self.coeffs[2*self.N: 3*self.N]

return ([r"$\sigma_x^%d$" % n for n in range(self.N)] +
[r"$\sigma_z^%d$" % n for n in range(self.N)] +
[r"$\sigma_x^%d\sigma_x^{%d} + \sigma_y^%d\sigma_y^{%d}$"