Source code for qutip.qip.device.cavityqed

# This file is part of QuTiP: Quantum Toolbox in Python.
#
#    Copyright (c) 2011 and later, Paul D. Nation and Robert J. Johansson.
#    All rights reserved.
#
#    Redistribution and use in source and binary forms, with or without
#    modification, are permitted provided that the following conditions are
#    met:
#
#    1. Redistributions of source code must retain the above copyright notice,
#       this list of conditions and the following disclaimer.
#
#    2. Redistributions in binary form must reproduce the above copyright
#       notice, this list of conditions and the following disclaimer in the
#       documentation and/or other materials provided with the distribution.
#
#    3. Neither the name of the QuTiP: Quantum Toolbox in Python nor the names
#       of its contributors may be used to endorse or promote products derived
#       from this software without specific prior written permission.
#
#    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
#    "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
#    LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
#    PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
#    HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
#    SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
#    LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
#    DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
#    THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
#    (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
#    OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
###############################################################################
import warnings
from copy import deepcopy

import numpy as np

from qutip.operators import tensor, identity, destroy, sigmax, sigmaz
from qutip.states import basis
from qutip.qip.circuit import QubitCircuit, Gate
from qutip.qip.device.processor import Processor
from qutip.qip.device.modelprocessor import ModelProcessor
from qutip.qip.operations import expand_operator
from qutip.qobj import Qobj
from qutip.qobjevo import QobjEvo
from qutip.qip.pulse import Pulse
from qutip.qip.compiler.gatecompiler import GateCompiler
from qutip.qip.compiler import CavityQEDCompiler


__all__ = ['DispersiveCavityQED']


[docs]class DispersiveCavityQED(ModelProcessor): """ The processor based on the physical implementation of a dispersive cavity QED system. The available Hamiltonian of the system is predefined. For a given pulse amplitude matrix, the processor can calculate the state evolution under the given control pulse, either analytically or numerically. (Only additional attributes are documented here, for others please refer to the parent class :class:`.ModelProcessor`) Parameters ---------- N: int The number of qubits in the system. correct_global_phase: float, optional Save the global phase, the analytical solution will track the global phase. It has no effect on the numerical solution. num_levels: int, optional The number of energy levels in the resonator. deltamax: int or list, optional The coefficients of sigma-x for each of the qubits in the system. epsmax: int or list, optional The coefficients of sigma-z for each of the qubits in the system. w0: int, optional The base frequency of the resonator. eps: int or list, optional The epsilon for each of the qubits in the system. delta: int or list, optional The epsilon for each of the qubits in the system. g: int or list, optional The interaction strength for each of the qubit with the resonator. t1: list or float Characterize the decoherence of amplitude damping for each qubit. A list of size `N` or a float for all qubits. t2: list of float Characterize the decoherence of dephasing for each qubit. A list of size `N` or a float for all qubits. Attributes ---------- sx_ops: list A list of sigmax Hamiltonians for each qubit. sz_ops: list A list of sigmaz Hamiltonians for each qubit. cavityqubit_ops: list A list of interacting Hamiltonians between cavity and each qubit. sx_u: array_like Pulse matrix for sigmax Hamiltonians. sz_u: array_like Pulse matrix for sigmaz Hamiltonians. g_u: array_like Pulse matrix for interacting Hamiltonians between cavity and each qubit. wq: list of float The frequency of the qubits calculated from eps and delta for each qubit. Delta: list of float The detuning with respect to w0 calculated from wq and w0 for each qubit. """ def __init__(self, N, correct_global_phase=True, num_levels=10, deltamax=1.0, epsmax=9.5, w0=10., wq=None, eps=9.5, delta=0.0, g=0.01, t1=None, t2=None): super(DispersiveCavityQED, 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" self.num_levels = num_levels self._params = {} self.set_up_params( N=N, num_levels=num_levels, deltamax=deltamax, epsmax=epsmax, w0=w0, wq=wq, eps=eps, delta=delta, g=g) self.set_up_ops(N) self.dims = [num_levels] + [2] * N
[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 # single qubit terms for m in range(N): self.pulses.append( Pulse(sigmax(), [m+1], spline_kind=self.spline_kind)) self.pulse_dict["sx" + str(m)] = index index += 1 for m in range(N): self.pulses.append( Pulse(sigmaz(), [m+1], spline_kind=self.spline_kind)) self.pulse_dict["sz" + str(m)] = index index += 1 # coupling terms a = tensor( [destroy(self.num_levels)] + [identity(2) for n in range(N)]) for n in range(N): sm = tensor([identity(self.num_levels)] + [destroy(2) if m == n else identity(2) for m in range(N)]) self.pulses.append( Pulse(a.dag() * sm + a * sm.dag(), list(range(N+1)), spline_kind=self.spline_kind)) self.pulse_dict["g" + str(n)] = index index += 1
[docs] def set_up_params( self, N, num_levels, deltamax, epsmax, w0, wq, eps, delta, g): """ Save the parameters in the attribute `params` and check the validity. The keys of `params` including "sx", "sz", "w0", "eps", "delta" and "g", each mapped to a list for parameters corresponding to each qubits. For coupling strength "g", list element i is the interaction between qubits i and i+1. Parameters ---------- N: int The number of qubits in the system. num_levels: int The number of energy levels in the resonator. deltamax: list The coefficients of sigma-x for each of the qubits in the system. epsmax: list The coefficients of sigma-z for each of the qubits in the system. wo: int The base frequency of the resonator. wq: list The frequency of the qubits. eps: list The epsilon for each of the qubits in the system. delta: list The delta for each of the qubits in the system. g: list The interaction strength for each of the qubit with the resonator. Notes ----- All parameters will be multiplied by 2*pi for simplicity """ sx_para = 2 * np.pi * self.to_array(deltamax, N) self._params["sx"] = sx_para sz_para = 2 * np.pi * self.to_array(epsmax, N) self._params["sz"] = sz_para w0 = 2 * np.pi * w0 self._params["w0"] = w0 eps = 2 * np.pi * self.to_array(eps, N) self._params["eps"] = eps delta = 2 * np.pi * self.to_array(delta, N) self._params["delta"] = delta g = 2 * np.pi * self.to_array(g, N) self._params["g"] = g # computed self.wq = np.sqrt(eps**2 + delta**2) self.Delta = self.wq - w0 # rwa/dispersive regime tests if any(g / (w0 - self.wq) > 0.05): warnings.warn("Not in the dispersive regime") if any((w0 - self.wq)/(w0 + self.wq) > 0.05): warnings.warn( "The rotating-wave approximation might not be valid.")
@property def sx_ops(self): return self.ctrls[0: self.N] @property def sz_ops(self): return self.ctrls[self.N: 2*self.N] @property def cavityqubit_ops(self): return self.ctrls[2*self.N: 3*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 g_u(self): return self.coeffs[2*self.N: 3*self.N]
[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"$g_{%d}$" % (n) for n in range(self.N)]])
[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.qc0.resolve_gates( basis=["SQRTISWAP", "ISWAP", "RX", "RZ"]) return self.qc1
[docs] def eliminate_auxillary_modes(self, U): """ Eliminate the auxillary modes like the cavity modes in cqed. """ psi_proj = tensor( [basis(self.num_levels, 0)] + [identity(2) for n in range(self.N)]) return psi_proj.dag() * U * psi_proj
[docs] def load_circuit( self, qc, 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. 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 = CavityQEDCompiler( self.N, self._params, pulse_dict=deepcopy(self.pulse_dict), global_phase=0.) 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