Source code for pennylane.ops.channel

# Copyright 2018-2021 Xanadu Quantum Technologies Inc.

# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at

#     http://www.apache.org/licenses/LICENSE-2.0

# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
This module contains the available built-in noisy
quantum channels supported by PennyLane, as well as their conventions.
"""
import numpy as np

from pennylane.operation import AnyWires, Channel


[docs]class AmplitudeDamping(Channel): r"""AmplitudeDamping(gamma, wires) Single-qubit amplitude damping error channel. Interaction with the environment can lead to changes in the state populations of a qubit. This is the phenomenon behind scattering, dissipation, attenuation, and spontaneous emission. It can be modelled by the amplitude damping channel, with the following Kraus matrices: .. math:: K_0 = \begin{bmatrix} 1 & 0 \\ 0 & \sqrt{1-\gamma} \end{bmatrix} .. math:: K_1 = \begin{bmatrix} 0 & \sqrt{\gamma} \\ 0 & 0 \end{bmatrix} where :math:`\gamma \in [0, 1]` is the amplitude damping probability. **Details:** * Number of wires: 1 * Number of parameters: 1 Args: gamma (float): amplitude damping probability wires (Sequence[int] or int): the wire the channel acts on """ num_params = 1 num_wires = 1 par_domain = "R" grad_method = "F" @classmethod def _kraus_matrices(cls, *params): gamma = params[0] if not 0.0 <= gamma <= 1.0: raise ValueError("gamma must be between [0,1].") K0 = np.diag([1, np.sqrt(1 - gamma)]) K1 = np.sqrt(gamma) * np.array([[0, 1], [0, 0]]) return [K0, K1]
[docs]class GeneralizedAmplitudeDamping(Channel): r"""GeneralizedAmplitudeDamping(gamma, p, wires) Single-qubit generalized amplitude damping error channel. This channel models the exchange of energy between a qubit and its environment at finite temperatures, with the following Kraus matrices: .. math:: K_0 = \sqrt{p} \begin{bmatrix} 1 & 0 \\ 0 & \sqrt{1-\gamma} \end{bmatrix} .. math:: K_1 = \sqrt{p}\begin{bmatrix} 0 & \sqrt{\gamma} \\ 0 & 0 \end{bmatrix} .. math:: K_2 = \sqrt{1-p}\begin{bmatrix} \sqrt{1-\gamma} & 0 \\ 0 & 1 \end{bmatrix} .. math:: K_3 = \sqrt{1-p}\begin{bmatrix} 0 & 0 \\ \sqrt{\gamma} & 0 \end{bmatrix} where :math:`\gamma \in [0, 1]` is the probability of damping and :math:`p \in [0, 1]` is the probability of the system being excited by the environment. **Details:** * Number of wires: 1 * Number of parameters: 2 Args: gamma (float): amplitude damping probability p (float): excitation probability wires (Sequence[int] or int): the wire the channel acts on """ num_params = 2 num_wires = 1 par_domain = "R" grad_method = "F" @classmethod def _kraus_matrices(cls, *params): gamma, p = params if not 0.0 <= gamma <= 1.0: raise ValueError("gamma must be between [0,1].") if not 0.0 <= p <= 1.0: raise ValueError("p must be between [0,1].") K0 = np.sqrt(p) * np.diag([1, np.sqrt(1 - gamma)]) K1 = np.sqrt(p) * np.sqrt(gamma) * np.array([[0, 1], [0, 0]]) K2 = np.sqrt(1 - p) * np.diag([np.sqrt(1 - gamma), 1]) K3 = np.sqrt(1 - p) * np.sqrt(gamma) * np.array([[0, 0], [1, 0]]) return [K0, K1, K2, K3]
[docs]class PhaseDamping(Channel): r"""PhaseDamping(gamma, wires) Single-qubit phase damping error channel. Interaction with the environment can lead to loss of quantum information changes without any changes in qubit excitations. This can be modelled by the phase damping channel, with the following Kraus matrices: .. math:: K_0 = \begin{bmatrix} 1 & 0 \\ 0 & \sqrt{1-\gamma} \end{bmatrix} .. math:: K_1 = \begin{bmatrix} 0 & 0 \\ 0 & \sqrt{\gamma} \end{bmatrix} where :math:`\gamma \in [0, 1]` is the phase damping probability. **Details:** * Number of wires: 1 * Number of parameters: 1 Args: gamma (float): phase damping probability wires (Sequence[int] or int): the wire the channel acts on """ num_params = 1 num_wires = 1 par_domain = "R" grad_method = "F" @classmethod def _kraus_matrices(cls, *params): gamma = params[0] if not 0.0 <= gamma <= 1.0: raise ValueError("gamma must be between [0,1].") K0 = np.diag([1, np.sqrt(1 - gamma)]) K1 = np.diag([0, np.sqrt(gamma)]) return [K0, K1]
[docs]class DepolarizingChannel(Channel): r"""DepolarizingChannel(p, wires) Single-qubit symmetrically depolarizing error channel. This channel is modelled by the following Kraus matrices: .. math:: K_0 = \sqrt{1-p} \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} .. math:: K_1 = \sqrt{p/3}\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} .. math:: K_2 = \sqrt{p/3}\begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix} .. math:: K_3 = \sqrt{p/3}\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} where :math:`p \in [0, 1]` is the depolarization probability and is equally divided in the application of all Pauli operations. **Details:** * Number of wires: 1 * Number of parameters: 1 Args: p (float): Each Pauli gate is applied with probability :math:`\frac{p}{3}` wires (Sequence[int] or int): the wire the channel acts on """ num_params = 1 num_wires = 1 par_domain = "R" grad_method = "A" grad_recipe = ([[1, 0, 1], [-1, 0, 0]],) @classmethod def _kraus_matrices(cls, *params): p = params[0] if not 0.0 <= p <= 1.0: raise ValueError("p must be between [0,1]") K0 = np.sqrt(1 - p) * np.eye(2) K1 = np.sqrt(p / 3) * np.array([[0, 1], [1, 0]]) K2 = np.sqrt(p / 3) * np.array([[0, -1j], [1j, 0]]) K3 = np.sqrt(p / 3) * np.array([[1, 0], [0, -1]]) return [K0, K1, K2, K3]
[docs]class BitFlip(Channel): r"""BitFlip(p, wires) Single-qubit bit flip (Pauli :math:`X`) error channel. This channel is modelled by the following Kraus matrices: .. math:: K_0 = \sqrt{1-p} \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} .. math:: K_1 = \sqrt{p}\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} where :math:`p \in [0, 1]` is the probability of a bit flip (Pauli :math:`X` error). **Details:** * Number of wires: 1 * Number of parameters: 1 Args: p (float): The probability that a bit flip error occurs. wires (Sequence[int] or int): the wire the channel acts on """ num_params = 1 num_wires = 1 par_domain = "R" grad_method = "A" grad_recipe = ([[1, 0, 1], [-1, 0, 0]],) @classmethod def _kraus_matrices(cls, *params): p = params[0] if not 0.0 <= p <= 1.0: raise ValueError("p must be between [0,1]") K0 = np.sqrt(1 - p) * np.eye(2) K1 = np.sqrt(p) * np.array([[0, 1], [1, 0]]) return [K0, K1]
[docs]class ResetError(Channel): r"""ResetError(p_0, p_1, wires) Single-qubit Reset error channel. This channel is modelled by the following Kraus matrices: .. math:: K_0 = \sqrt{1-p_0-p_1} \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} .. math:: K_1 = \sqrt{p_0}\begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix} .. math:: K_2 = \sqrt{p_0}\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix} .. math:: K_3 = \sqrt{p_1}\begin{bmatrix} 0 & 0 \\ 1 & 0 \end{bmatrix} .. math:: K_4 = \sqrt{p_1}\begin{bmatrix} 0 & 0 \\ 0 & 1 \end{bmatrix} where :math:`p_0 \in [0, 1]` is the probability of a reset to 0, and :math:`p_1 \in [0, 1]` is the probability of a reset to 1 error. **Details:** * Number of wires: 1 * Number of parameters: 2 Args: p_0 (float): The probability that a reset to 0 error occurs. p_1 (float): The probability that a reset to 1 error occurs. wires (Sequence[int] or int): the wire the channel acts on """ num_params = 2 num_wires = 1 par_domain = "R" grad_method = "F" @classmethod def _kraus_matrices(cls, *params): p_0, p_1 = params[0], params[1] if not 0.0 <= p_0 <= 1.0: raise ValueError("p_0 must be between [0,1]") if not 0.0 <= p_1 <= 1.0: raise ValueError("p_1 must be between [0,1]") if not 0.0 <= p_0 + p_1 <= 1.0: raise ValueError("p_0 + p_1 must be between [0,1]") K0 = np.sqrt(1 - p_0 - p_1) * np.eye(2) K1 = np.sqrt(p_0) * np.array([[1, 0], [0, 0]]) K2 = np.sqrt(p_0) * np.array([[0, 1], [0, 0]]) K3 = np.sqrt(p_1) * np.array([[0, 0], [1, 0]]) K4 = np.sqrt(p_1) * np.array([[0, 0], [0, 1]]) return [K0, K1, K2, K3, K4]
[docs]class PhaseFlip(Channel): r"""PhaseFlip(p, wires) Single-qubit bit flip (Pauli :math:`Z`) error channel. This channel is modelled by the following Kraus matrices: .. math:: K_0 = \sqrt{1-p} \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} .. math:: K_1 = \sqrt{p}\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} where :math:`p \in [0, 1]` is the probability of a phase flip (Pauli :math:`Z`) error. **Details:** * Number of wires: 1 * Number of parameters: 1 Args: p (float): The probability that a phase flip error occurs. wires (Sequence[int] or int): the wire the channel acts on """ num_params = 1 num_wires = 1 par_domain = "R" grad_method = "A" grad_recipe = ([[1, 0, 1], [-1, 0, 0]],) @classmethod def _kraus_matrices(cls, *params): p = params[0] if not 0.0 <= p <= 1.0: raise ValueError("p must be between [0,1]") K0 = np.sqrt(1 - p) * np.eye(2) K1 = np.sqrt(p) * np.array([[1, 0], [0, -1]]) return [K0, K1]
[docs]class QubitChannel(Channel): r"""QubitChannel(K_list, wires) Apply an arbitrary fixed quantum channel. Kraus matrices that represent the fixed channel are provided as a list of NumPy arrays. **Details:** * Number of wires: Any (the operation can act on any number of wires) * Number of parameters: 1 * Gradient recipe: None Args: K_list (list[array[complex]]): List of Kraus matrices wires (Union[Wires, Sequence[int], or int]): the wire(s) the operation acts on """ num_params = 1 num_wires = AnyWires par_domain = "L" grad_method = None def __init__(self, *params, wires=None, do_queue=True): super().__init__(*params, wires=wires, do_queue=do_queue) K_list = params[0] # check all Kraus matrices are square matrices if not all(K.shape[0] == K.shape[1] for K in K_list): raise ValueError( "Only channels with the same input and output Hilbert space dimensions can be applied." ) # check all Kraus matrices have the same shape if not all(K.shape == K_list[0].shape for K in K_list): raise ValueError("All Kraus matrices must have the same shape.") # check the dimension of all Kraus matrices are valid if not all(K.ndim == 2 for K in K_list): raise ValueError( "Dimension of all Kraus matrices must be (2**num_wires, 2**num_wires)." ) # check that the channel represents a trace-preserving map K_arr = np.array(K_list) Kraus_sum = np.einsum("ajk,ajl->kl", K_arr.conj(), K_arr) if not np.allclose(Kraus_sum, np.eye(K_list[0].shape[0])): raise ValueError("Only trace preserving channels can be applied.") @classmethod def _kraus_matrices(cls, *params): K_list = params[0] return K_list
__qubit_channels__ = { "AmplitudeDamping", "GeneralizedAmplitudeDamping", "PhaseDamping", "DepolarizingChannel", "BitFlip", "PhaseFlip", "ResetError", "QubitChannel", } __all__ = list(__qubit_channels__)