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This code is part of Qiskit.","#","# (C) Copyright IBM 2017, 2019.","#","# This code is licensed under the Apache License, Version 2.0. You may","# obtain a copy of this license in the LICENSE.txt file in the root directory","# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.","#","# Any modifications or derivative works of this code must retain this","# copyright notice, and modified files need to carry a notice indicating","# that they have been altered from the originals.","","\"\"\"","Kraus representation of a Quantum Channel.","\"\"\"","","from __future__ import annotations","import copy","from numbers import Number","import numpy as np","","from qiskit import circuit","from qiskit.circuit.quantumcircuit import QuantumCircuit","from qiskit.circuit.instruction import Instruction","from qiskit.exceptions import QiskitError","from qiskit.quantum_info.operators.predicates import is_identity_matrix","from qiskit.quantum_info.operators.channel.quantum_channel import QuantumChannel","from qiskit.quantum_info.operators.op_shape import OpShape","from qiskit.quantum_info.operators.channel.choi import Choi","from qiskit.quantum_info.operators.channel.superop import SuperOp","from qiskit.quantum_info.operators.channel.transformations import _to_kraus","from qiskit.quantum_info.operators.mixins import generate_apidocs","from qiskit.quantum_info.operators.base_operator import BaseOperator","","","class Kraus(QuantumChannel):"," r\"\"\"Kraus representation of a quantum channel.",""," For a quantum channel :math:`\\mathcal{E}`, the Kraus representation is"," given by a set of matrices :math:`[A_0,...,A_{K-1}]` such that the"," evolution of a :class:`~qiskit.quantum_info.DensityMatrix`"," :math:`\\rho` is given by",""," .. math::",""," \\mathcal{E}(\\rho) = \\sum_{i=0}^{K-1} A_i \\rho A_i^\\dagger",""," A general operator map :math:`\\mathcal{G}` can also be written using the"," generalized Kraus representation which is given by two sets of matrices"," :math:`[A_0,...,A_{K-1}]`, :math:`[B_0,...,A_{B-1}]` such that",""," .. math::",""," \\mathcal{G}(\\rho) = \\sum_{i=0}^{K-1} A_i \\rho B_i^\\dagger",""," See reference [1] for further details.",""," References:"," 1. C.J. Wood, J.D. Biamonte, D.G. Cory, *Tensor networks and graphical calculus"," for open quantum systems*, Quant. Inf. Comp. 15, 0579-0811 (2015)."," `arXiv:1111.6950 [quant-ph] `_"," \"\"\"",""," def __init__("," self,"," data: QuantumCircuit | circuit.instruction.Instruction | BaseOperator | np.ndarray,"," input_dims: tuple | None = None,"," output_dims: tuple | None = None,"," ):"," \"\"\"Initialize a quantum channel Kraus operator.",""," Args:"," data: data to initialize superoperator."," input_dims: the input subsystem dimensions."," output_dims: the output subsystem dimensions.",""," Raises:"," QiskitError: if input data cannot be initialized as a list of Kraus matrices.",""," Additional Information:"," If the input or output dimensions are None, they will be"," automatically determined from the input data. If the input data is"," a list of Numpy arrays of shape :math:`(2^N,\\\\,2^N)` qubit systems will be"," used. If the input does not correspond to an N-qubit channel, it"," will assign a single subsystem with dimension specified by the"," shape of the input."," \"\"\""," # If the input is a list or tuple we assume it is a list of Kraus"," # matrices, if it is a numpy array we assume that it is a single Kraus"," # operator"," # TODO properly handle array construction from ragged data (like tuple(np.ndarray, None))"," # and document these accepted input cases. See also Qiskit/qiskit-terra#9307."," if isinstance(data, (list, tuple, np.ndarray)):"," # Check if it is a single unitary matrix A for channel:"," # E(rho) = A * rho * A^\\dagger"," if _is_matrix(data):"," # Convert single Kraus op to general Kraus pair"," kraus = ([np.asarray(data, dtype=complex)], None)"," shape = kraus[0][0].shape",""," # Check if single Kraus set [A_i] for channel:"," # E(rho) = sum_i A_i * rho * A_i^dagger"," elif isinstance(data, list) and len(data) > 0:"," # Get dimensions from first Kraus op"," kraus = [np.asarray(data[0], dtype=complex)]"," shape = kraus[0].shape"," # Iterate over remaining ops and check they are same shape"," for i in data[1:]:"," op = np.asarray(i, dtype=complex)"," if op.shape != shape:"," raise QiskitError(\"Kraus operators are different dimensions.\")"," kraus.append(op)"," # Convert single Kraus set to general Kraus pair"," kraus = (kraus, None)",""," # Check if generalized Kraus set ([A_i], [B_i]) for channel:"," # E(rho) = sum_i A_i * rho * B_i^dagger"," elif isinstance(data, tuple) and len(data) == 2 and len(data[0]) > 0:"," kraus_left = [np.asarray(data[0][0], dtype=complex)]"," shape = kraus_left[0].shape"," for i in data[0][1:]:"," op = np.asarray(i, dtype=complex)"," if op.shape != shape:"," raise QiskitError(\"Kraus operators are different dimensions.\")"," kraus_left.append(op)"," if data[1] is None:"," kraus = (kraus_left, None)"," else:"," kraus_right = []"," for i in data[1]:"," op = np.asarray(i, dtype=complex)"," if op.shape != shape:"," raise QiskitError(\"Kraus operators are different dimensions.\")"," kraus_right.append(op)"," kraus = (kraus_left, kraus_right)"," else:"," raise QiskitError(\"Invalid input for Kraus channel.\")"," op_shape = OpShape.auto(dims_l=output_dims, dims_r=input_dims, shape=kraus[0][0].shape)"," else:"," # Otherwise we initialize by conversion from another Qiskit"," # object into the QuantumChannel."," if isinstance(data, (QuantumCircuit, Instruction)):"," # If the input is a Terra QuantumCircuit or Instruction we"," # convert it to a SuperOp"," data = SuperOp._init_instruction(data)"," else:"," # We use the QuantumChannel init transform to initialize"," # other objects into a QuantumChannel or Operator object."," data = self._init_transformer(data)"," op_shape = data._op_shape"," output_dim, input_dim = op_shape.shape"," # Now that the input is an operator we convert it to a Kraus"," rep = getattr(data, \"_channel_rep\", \"Operator\")"," kraus = _to_kraus(rep, data._data, input_dim, output_dim)",""," # Initialize either single or general Kraus"," if kraus[1] is None or np.allclose(kraus[0], kraus[1]):"," # Standard Kraus map"," data = (kraus[0], None)"," else:"," # General (non-CPTP) Kraus map"," data = kraus"," super().__init__(data, op_shape=op_shape)",""," @property"," def data(self):"," \"\"\"Return list of Kraus matrices for channel.\"\"\""," if self._data[1] is None:"," # If only a single Kraus set, don't return the tuple"," # Just the fist set"," return self._data[0]"," else:"," # Otherwise return the tuple of both kraus sets"," return self._data",""," def is_cptp(self, atol=None, rtol=None):"," \"\"\"Return True if completely-positive trace-preserving.\"\"\""," if self._data[1] is not None:"," return False"," if atol is None:"," atol = self.atol"," if rtol is None:"," rtol = self.rtol"," accum = 0j"," for op in self._data[0]:"," accum += np.dot(np.transpose(np.conj(op)), op)"," return is_identity_matrix(accum, rtol=rtol, atol=atol)",""," def _evolve(self, state, qargs=None):"," return SuperOp(self)._evolve(state, qargs)",""," # ---------------------------------------------------------------------"," # BaseOperator methods"," # ---------------------------------------------------------------------",""," def conjugate(self):"," ret = copy.copy(self)"," kraus_l, kraus_r = self._data"," kraus_l = [np.conj(k) for k in kraus_l]"," if kraus_r is not None:"," kraus_r = [k.conj() for k in kraus_r]"," ret._data = (kraus_l, kraus_r)"," return ret",""," def transpose(self):"," ret = copy.copy(self)"," ret._op_shape = self._op_shape.transpose()"," kraus_l, kraus_r = self._data"," kraus_l = [np.transpose(k) for k in kraus_l]"," if kraus_r is not None:"," kraus_r = [np.transpose(k) for k in kraus_r]"," ret._data = (kraus_l, kraus_r)"," return ret",""," def adjoint(self):"," ret = copy.copy(self)"," ret._op_shape = self._op_shape.transpose()"," kraus_l, kraus_r = self._data"," kraus_l = [np.conj(np.transpose(k)) for k in kraus_l]"," if kraus_r is not None:"," kraus_r = [np.conj(np.transpose(k)) for k in kraus_r]"," ret._data = (kraus_l, kraus_r)"," return ret",""," def compose(self, other: Kraus, qargs: list | None = None, front: bool = False) -> Kraus:"," if qargs is None:"," qargs = getattr(other, \"qargs\", None)"," if qargs is not None:"," return Kraus(SuperOp(self).compose(other, qargs=qargs, front=front))",""," if not isinstance(other, Kraus):"," other = Kraus(other)"," new_shape = self._op_shape.compose(other._op_shape, qargs, front)"," input_dims = new_shape.dims_r()"," output_dims = new_shape.dims_l()",""," if front:"," ka_l, ka_r = self._data"," kb_l, kb_r = other._data"," else:"," ka_l, ka_r = other._data"," kb_l, kb_r = self._data",""," kab_l = [np.dot(a, b) for a in ka_l for b in kb_l]"," if ka_r is None and kb_r is None:"," kab_r = None"," elif ka_r is None:"," kab_r = [np.dot(a, b) for a in ka_l for b in kb_r]"," elif kb_r is None:"," kab_r = [np.dot(a, b) for a in ka_r for b in kb_l]"," else:"," kab_r = [np.dot(a, b) for a in ka_r for b in kb_r]"," ret = Kraus((kab_l, kab_r), input_dims, output_dims)"," ret._op_shape = new_shape"," return ret",""," def tensor(self, other: Kraus) -> Kraus:"," if not isinstance(other, Kraus):"," other = Kraus(other)"," return self._tensor(self, other)",""," def expand(self, other: Kraus) -> Kraus:"," if not isinstance(other, Kraus):"," other = Kraus(other)"," return self._tensor(other, self)",""," @classmethod"," def _tensor(cls, a, b):"," ret = copy.copy(a)"," ret._op_shape = a._op_shape.tensor(b._op_shape)",""," # Get tensor matrix"," ka_l, ka_r = a._data"," kb_l, kb_r = b._data"," kab_l = [np.kron(ka, kb) for ka in ka_l for kb in kb_l]"," if ka_r is None and kb_r is None:"," kab_r = None"," else:"," if ka_r is None:"," ka_r = ka_l"," if kb_r is None:"," kb_r = kb_l"," kab_r = [np.kron(a, b) for a in ka_r for b in kb_r]"," ret._data = (kab_l, kab_r)"," return ret",""," def __add__(self, other):"," qargs = getattr(other, \"qargs\", None)"," if not isinstance(other, QuantumChannel):"," other = Choi(other)"," return self._add(other, qargs=qargs)",""," def __sub__(self, other):"," qargs = getattr(other, \"qargs\", None)"," if not isinstance(other, QuantumChannel):"," other = Choi(other)"," return self._add(-other, qargs=qargs)",""," def _add(self, other, qargs=None):"," # Since we cannot directly add two channels in the Kraus"," # representation we try and use the other channels method"," # or 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docstrings for API 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