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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.","\"\"\"","Stinespring representation of a Quantum Channel.","\"\"\"","","from __future__ import annotations","import copy","from numbers import Number","import numpy as np","","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.kraus import Kraus","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_stinespring","from qiskit.quantum_info.operators.mixins import generate_apidocs","from qiskit.quantum_info.operators.base_operator import BaseOperator","","","class Stinespring(QuantumChannel):"," r\"\"\"Stinespring representation of a quantum channel.",""," The Stinespring representation of a quantum channel :math:`\\mathcal{E}`"," is a rectangular matrix :math:`A` such that the evolution of a"," :class:`~qiskit.quantum_info.DensityMatrix` :math:`\\rho` is given by",""," .. math::",""," \\mathcal{E}(ρ) = \\mbox{Tr}_2\\left[A ρ A^\\dagger\\right]",""," where :math:`\\mbox{Tr}_2` is the :func:`partial_trace` over subsystem 2.",""," A general operator map :math:`\\mathcal{G}` can also be written using the"," generalized Stinespring representation which is given by two matrices"," :math:`A`, :math:`B` such that",""," .. math::",""," \\mathcal{G}(ρ) = \\mbox{Tr}_2\\left[A ρ B^\\dagger\\right]",""," 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 | Instruction | BaseOperator | np.ndarray,"," input_dims: int | tuple | None = None,"," output_dims: int | tuple | None = None,"," ):"," \"\"\"Initialize a quantum channel Stinespring operator.",""," Args:"," data (QuantumCircuit or"," Instruction or"," BaseOperator or"," matrix): data to initialize superoperator."," input_dims (tuple): the input subsystem dimensions."," [Default: None]"," output_dims (tuple): the output subsystem dimensions."," [Default: None]",""," Raises:"," QiskitError: if input data cannot be initialized as a"," a list of Kraus matrices.",""," Additional Information:"," If the input or output dimensions are None, they will be"," automatically determined from the input data. This can fail for the"," Stinespring operator if the output dimension cannot be automatically"," determined."," \"\"\""," # If the input is a list or tuple we assume it is a pair of general"," # Stinespring matrices. If it is a numpy array we assume that it is"," # a single Stinespring matrix."," if isinstance(data, (list, tuple, np.ndarray)):"," if not isinstance(data, tuple):"," # Convert single Stinespring set to length 1 tuple"," stine = (np.asarray(data, dtype=complex), None)"," if isinstance(data, tuple) and len(data) == 2:"," if data[1] is None:"," stine = (np.asarray(data[0], dtype=complex), None)"," else:"," stine = (np.asarray(data[0], dtype=complex), np.asarray(data[1], dtype=complex))",""," dim_left, dim_right = stine[0].shape"," # If two Stinespring matrices check they are same shape"," if stine[1] is not None:"," if stine[1].shape != (dim_left, dim_right):"," raise QiskitError(\"Invalid Stinespring input.\")"," input_dim = dim_right"," if output_dims:"," output_dim = np.prod(output_dims)"," else:"," output_dim = input_dim"," if dim_left % output_dim != 0:"," raise QiskitError(\"Invalid output_dim\")"," op_shape = OpShape.auto("," dims_l=output_dims, dims_r=input_dims, shape=(output_dim, input_dim)"," )"," 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 intialize"," # 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"," # Stinespring operator"," rep = getattr(data, \"_channel_rep\", \"Operator\")"," stine = _to_stinespring(rep, data._data, input_dim, output_dim)",""," # Initialize either single or general Stinespring"," if stine[1] is None or (stine[1] == stine[0]).all():"," # Standard Stinespring map"," data = (stine[0], None)"," else:"," # General (non-CPTP) Stinespring map"," data = stine"," super().__init__(data, op_shape=op_shape)",""," @property"," def data(self):"," # Override to deal with data being either tuple or not"," if self._data[1] is None:"," return self._data[0]"," else:"," return self._data",""," def is_cptp(self, atol=None, rtol=None):"," \"\"\"Return True if completely-positive trace-preserving.\"\"\""," if atol is None:"," atol = self.atol"," if rtol is None:"," rtol = self.rtol"," if self._data[1] is not None:"," return False"," check = np.dot(np.transpose(np.conj(self._data[0])), self._data[0])"," return is_identity_matrix(check, rtol=self.rtol, atol=self.atol)",""," def _evolve(self, state, qargs=None):"," return SuperOp(self)._evolve(state, qargs)",""," # ---------------------------------------------------------------------"," # BaseOperator methods"," # ---------------------------------------------------------------------",""," def conjugate(self):"," ret = copy.copy(self)"," stine_l = np.conjugate(self._data[0])"," stine_r = None"," if self._data[1] is not None:"," stine_r = np.conjugate(self._data[1])"," ret._data = (stine_l, stine_r)"," return ret",""," def transpose(self):"," ret = copy.copy(self)"," ret._op_shape = self._op_shape.transpose()"," din, dout = self.dim"," dtr = self._data[0].shape[0] // dout"," stine = [None, None]"," for i, mat in enumerate(self._data):"," if mat is not None:"," stine[i] = np.reshape("," np.transpose(np.reshape(mat, (dout, dtr, din)), (2, 1, 0)), (din * dtr, dout)"," )"," ret._data = (stine[0], stine[1])"," return ret",""," def compose("," self, other: Stinespring, qargs: list | None = None, front: bool = False"," ) -> Stinespring:"," if qargs is None:"," qargs = getattr(other, \"qargs\", None)"," if qargs is not None:"," return Stinespring(SuperOp(self).compose(other, qargs=qargs, front=front))"," # Otherwise we convert via Kraus representation rather than"," # superoperator to avoid unnecessary representation conversions"," return Stinespring(Kraus(self).compose(other, front=front))",""," def tensor(self, other: Stinespring) -> Stinespring:"," if not isinstance(other, Stinespring):"," other = Stinespring(other)"," return self._tensor(self, other)",""," def expand(self, other: Stinespring) -> Stinespring:"," if not isinstance(other, Stinespring):"," other = Stinespring(other)"," return self._tensor(other, self)",""," @classmethod"," def _tensor(cls, a, b):"," # Tensor Stinespring ops"," sa_l, sa_r = a._data"," sb_l, sb_r = b._data",""," # Reshuffle tensor dimensions"," din_a, dout_a = a.dim"," din_b, dout_b = b.dim"," dtr_a = sa_l.shape[0] // dout_a"," dtr_b = sb_l.shape[0] // dout_b",""," shape_in = (dout_a, dtr_a, dout_b, dtr_b, din_a * din_b)"," shape_out = (dout_a * dtr_a * dout_b * dtr_b, din_a * din_b)"," sab_l = np.kron(sa_l, sb_l)"," # Reravel indices"," sab_l = np.reshape(np.transpose(np.reshape(sab_l, shape_in), (0, 2, 1, 3, 4)), shape_out)",""," # Compute right Stinespring op"," if sa_r is None and sb_r is None:"," sab_r = None"," else:"," if sa_r is None:"," sa_r = sa_l"," elif sb_r is None:"," sb_r = sb_l"," sab_r = np.kron(sa_r, sb_r)"," # Reravel indices"," sab_r = np.reshape("," np.transpose(np.reshape(sab_r, shape_in), (0, 2, 1, 3, 4)), shape_out"," )"," ret = copy.copy(a)"," ret._op_shape = a._op_shape.tensor(b._op_shape)"," ret._data = (sab_l, sab_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 Stinespring"," # representation we convert to the Choi representation"," return Stinespring(Choi(self)._add(other, qargs=qargs))",""," def _multiply(self, other):"," if not isinstance(other, 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