Source code for qutip.qip.device.spinchain

from copy import deepcopy

import numpy as np

from qutip.operators import sigmax, sigmay, sigmaz
from qutip.tensor import tensor
from qutip.qip.circuit import QubitCircuit
from qutip.qip.device.modelprocessor import ModelProcessor
from qutip.qip.pulse import Pulse
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.device.LinearSpinChain` and :class:`qutip.qip.device.CircularSpinChain`. (Only additional attributes are documented here, for others please refer to the parent class :class:`.ModelProcessor`) Parameters ---------- N: int The number of qubits in the system. correct_global_phase: float Save the global phase, the analytical solution will track the global phase. It has no effect on the numerical solution. sx: int or list The delta for each of the qubits in the system. sz: int or list The epsilon for each of the qubits in the system. sxsy: int or list The interaction strength for each of the qubit pair in the system. t1: list or float Characterize the decoherence of amplitude damping for each qubit. A list of size `N` or a float for all qubits. t2: list of float Characterize the decoherence of dephasing for each qubit. A list of size `N` or a float for all qubits. Attributes ---------- sx: list The delta for each of the qubits in the system. sz: list The epsilon for each of the qubits in the system. sxsy: list The interaction strength for each of the qubit pair in the system. sx_ops: list A list of sigmax Hamiltonians for each qubit. sz_ops: list A list of sigmaz Hamiltonians for each qubit. sxsy_ops: list A list of tensor(sigmax, sigmay) interacting Hamiltonians for each qubit. sx_u: array_like Pulse matrix for sigmax Hamiltonians. sz_u: array_like Pulse matrix for sigmaz Hamiltonians. sxsy_u: array_like Pulse matrix for tensor(sigmax, sigmay) interacting Hamiltonians. """ 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. """ self.pulse_dict = {} index = 0 # sx_ops for m in range(N): self.pulses.append( Pulse(sigmax(), m, spline_kind=self.spline_kind)) self.pulse_dict["sx" + str(m)] = index index += 1 # sz_ops for m in range(N): self.pulses.append( Pulse(sigmaz(), m, spline_kind=self.spline_kind)) self.pulse_dict["sz" + str(m)] = index index += 1 # 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)) self.pulse_dict["g" + str(n)] = index index += 1
[docs] def set_up_params(self, sx, sz): """ Save the parameters in the attribute `params` and check the validity. The keys of `params` including "sx", "sz", and "sxsy", each mapped to a list for parameters corresponding to each qubits. For coupling strength "sxsy", list element i is the interaction between qubits i and i+1. Parameters ---------- sx: float or list The coefficient of sigmax in the model sz: flaot or list The coefficient of sigmaz in the model Notes ----- The coefficient of sxsy is defined in the submethods. All parameters will be multiplied by 2*pi for simplicity """ sx_para = 2 * np.pi * self.to_array(sx, self.N) self._params["sx"] = sx_para sz_para = 2 * np.pi * self.to_array(sz, self.N) self._params["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:]
[docs] def load_circuit( self, qc, setup, schedule_mode="ASAP", compiler=None): """ Decompose a :class:`.QubitCircuit` in to the control amplitude generating the corresponding evolution. Parameters ---------- qc: :class:`.QubitCircuit` Takes the quantum circuit to be implemented. setup: string "linear" or "circular" for two sub-classes. Returns ------- tlist: array_like A NumPy array specifies the time of each coefficient coeffs: array_like A 2d NumPy array of the shape (len(ctrls), len(tlist)). Each row corresponds to the control pulse sequence for one Hamiltonian. """ gates = self.optimize_circuit(qc).gates if compiler is None: compiler = SpinChainCompiler( self.N, self._params, setup=setup, global_phase=0., pulse_dict=deepcopy(self.pulse_dict)) tlist, coeffs = compiler.compile( gates, schedule_mode=schedule_mode) self.global_phase = compiler.global_phase self.coeffs = coeffs for i in range(len(coeffs)): self.pulses[i].tlist = tlist[i] return tlist, self.coeffs
[docs] def adjacent_gates(self, qc, setup="linear"): """ Method to resolve 2 qubit gates with non-adjacent control/s or target/s in terms of gates with adjacent interactions for linear/circular spin chain system. Parameters ---------- qc: :class:`.QubitCircuit` The circular spin chain circuit to be resolved setup: Boolean Linear of Circular spin chain setup Returns ------- qc: :class:`.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]: qc_t.add_gate(gate.name, targets=[i], controls=[i + 1]) else: qc_t.add_gate(gate.name, targets=[i + 1], 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. qc_t.add_gate("SWAP", targets=[i, i + 1]) if end == gate.controls[0]: qc_t.add_gate(gate.name, targets=[i + 1], controls=[i + 2]) else: qc_t.add_gate(gate.name, targets=[i + 2], controls=[i + 1]) qc_t.add_gate("SWAP", [i, 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", [i, i + 1]) 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]: temp.add_gate(gate.name, targets=[i], controls=[i + 1]) else: temp.add_gate(gate.name, targets=[i + 1], controls=[i]) elif (N + start - end - i - i == 2 and (N - end + start + 1) % 2 == 1): temp.add_gate("SWAP", targets=[i, i + 1]) if end == gate.controls[0]: temp.add_gate(gate.name, targets=[i + 2], controls=[i + 1]) else: temp.add_gate(gate.name, targets=[i + 1], controls=[i + 2]) temp.add_gate("SWAP", [i, i + 1]) i += 1 else: temp.add_gate("SWAP", [i, i + 1]) 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): if gate.name in ["CNOT", "CSIGN"]: qc_t.add_gate(gate.name, end + gate.targets[0], end + gate.controls[0]) else: qc_t.add_gate(gate.name, [end + gate.targets[0], end + gate.targets[1]]) elif (j == N - end - 2): if gate.name in ["CNOT", "CSIGN"]: qc_t.add_gate(gate.name, end + gate.targets[0], (end + gate.controls[0]) % N) else: qc_t.add_gate(gate.name, [end + gate.targets[0], (end + gate.targets[1]) % N]) else: if gate.name in ["CNOT", "CSIGN"]: qc_t.add_gate(gate.name, (end + gate.targets[0]) % N, (end + gate.controls[0]) % N) else: qc_t.add_gate(gate.name, [(end + gate.targets[0]) % N, (end + gate.targets[1]) % N]) j = j + 1 elif (end - start) == N - 1: qc_t.add_gate(gate.name, gate.targets, gate.controls) 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): qc_t.add_gate(gate.name, [i, i + 1]) elif ((start + end - i - i) == 2 and (end - start + 1) % 2 == 1): qc_t.add_gate("SWAP", [i, i + 1]) qc_t.add_gate(gate.name, [i + 1, i + 2]) qc_t.add_gate("SWAP", [i, i + 1]) i += 1 else: qc_t.add_gate("SWAP", [i, i + 1]) 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): temp.add_gate(gate.name, [i, i + 1]) elif (N + start - end - i - i == 2 and (N - end + start + 1) % 2 == 1): temp.add_gate("SWAP", [i, i + 1]) temp.add_gate(gate.name, [i + 1, i + 2]) temp.add_gate("SWAP", [i, i + 1]) i += 1 else: temp.add_gate("SWAP", [i, i + 1]) 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): qc_t.add_gate(gate.name, [end + gate.targets[0], end + gate.targets[1]]) elif(j == N - end - 2): qc_t.add_gate(gate.name, [end + gate.targets[0], (end + gate.targets[1]) % N]) else: qc_t.add_gate(gate.name, [(end + gate.targets[0]) % N, (end + gate.targets[1]) % N]) j = j + 1 else: qc_t.add_gate(gate.name, gate.targets, gate.controls, 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:`.QubitCircuit` Takes the quantum circuit to be implemented. Returns ------- qc: :class:`.QubitCircuit` The circuit representation with elementary gates that can be implemented in this model. """ self.qc0 = qc self.qc1 = self.adjacent_gates(self.qc0) 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 = 2 * np.pi * self.to_array(sxsy, self.N-1) self._params["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]
[docs] def load_circuit( self, qc, schedule_mode="ASAP", compiler=None): return super(LinearSpinChain, self).load_circuit( qc, "linear", schedule_mode=schedule_mode, compiler=compiler)
[docs] def get_operators_labels(self): """ Get the labels for each Hamiltonian. It is used in the method``plot_pulses``. It is a 2-d nested list, in the plot, a different color will be used for each sublist. """ 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 + 1, n, n + 1) for n in range(self.N - 1)], ])
[docs] def adjacent_gates(self, qc): return super(LinearSpinChain, self).adjacent_gates(qc, "linear")
[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): if N <= 1: raise ValueError( "Circuit spin chain must have at least 2 qubits. " "The number of qubits is increased to 2.") 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)) self.pulse_dict["g" + str(N-1)] = len(self.pulses) - 1
[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 = 2 * np.pi * self.to_array(sxsy, self.N) self._params["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]
[docs] def load_circuit( self, qc, schedule_mode="ASAP", compiler=None): return super(CircularSpinChain, self).load_circuit( qc, "circular", schedule_mode=schedule_mode, compiler=compiler)
[docs] def get_operators_labels(self): """ Get the labels for each Hamiltonian. It is used in the method``plot_pulses``. It is a 2-d nested list, in the plot, a different color will be used for each sublist. """ 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 + 1) % self.N, n, (n + 1) % self.N) for n in range(self.N)]])
[docs] def adjacent_gates(self, qc): return super(CircularSpinChain, self).adjacent_gates(qc, "circular")