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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.","","","\"\"\"","Chi-matrix representation of a Quantum Channel.","\"\"\"","","from __future__ import annotations","import copy","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.channel.quantum_channel import QuantumChannel","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_chi","from qiskit.quantum_info.operators.mixins import generate_apidocs","from qiskit.quantum_info.operators.base_operator import BaseOperator","","","class Chi(QuantumChannel):"," r\"\"\"Pauli basis Chi-matrix representation of a quantum channel.",""," The Chi-matrix representation of an :math:`n`-qubit quantum channel"," :math:`\\mathcal{E}` is a matrix :math:`\\chi` such that the evolution of a"," :class:`~qiskit.quantum_info.DensityMatrix` :math:`\\rho` is given by",""," .. math::",""," \\mathcal{E}(ρ) = \\frac{1}{2^n} \\sum_{i, j} \\chi_{i,j} P_i ρ P_j",""," where :math:`[P_0, P_1, ..., P_{4^{n}-1}]` is the :math:`n`-qubit Pauli basis in"," lexicographic order. It is related to the :class:`Choi` representation by a change"," of basis of the Choi-matrix into the Pauli basis. The :math:`\\frac{1}{2^n}`"," in the definition above is a normalization factor that arises from scaling the"," Pauli basis to make it orthonormal.",""," 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 Chi-matrix 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 is not an N-qubit channel or"," cannot be initialized as a Chi-matrix.",""," Additional Information:"," If the input or output dimensions are None, they will be"," automatically determined from the input data. The Chi matrix"," representation is only valid for N-qubit channels."," \"\"\""," # If the input is a raw list or matrix we assume that it is"," # already a Chi matrix."," if isinstance(data, (list, np.ndarray)):"," # Initialize from raw numpy or list matrix."," chi_mat = np.asarray(data, dtype=complex)"," # Determine input and output dimensions"," dim_l, dim_r = chi_mat.shape"," if dim_l != dim_r:"," raise QiskitError(\"Invalid Chi-matrix input.\")"," if input_dims:"," input_dim = np.prod(input_dims)"," if output_dims:"," output_dim = np.prod(input_dims)"," if output_dims is None and input_dims is None:"," output_dim = int(np.sqrt(dim_l))"," input_dim = dim_l // output_dim"," elif input_dims is None:"," input_dim = dim_l // output_dim"," elif output_dims is None:"," output_dim = dim_l // input_dim"," # Check dimensions"," if input_dim * output_dim != dim_l:"," raise QiskitError(\"Invalid shape for Chi-matrix input.\")"," 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)"," input_dim, output_dim = data.dim"," # Now that the input is an operator we convert it to a Chi object"," rep = getattr(data, \"_channel_rep\", \"Operator\")"," chi_mat = _to_chi(rep, data._data, input_dim, output_dim)"," if input_dims is None:"," input_dims = data.input_dims()"," if output_dims is None:"," output_dims = data.output_dims()"," # Check input is N-qubit channel"," num_qubits = int(np.log2(input_dim))"," if 2**num_qubits != input_dim or input_dim != output_dim:"," raise QiskitError(\"Input is not an n-qubit Chi matrix.\")"," super().__init__(chi_mat, num_qubits=num_qubits)",""," def __array__(self, dtype=None):"," if dtype:"," return np.asarray(self.data, dtype=dtype)"," return self.data",""," @property"," def _bipartite_shape(self):"," \"\"\"Return the shape for bipartite matrix\"\"\""," return (self._input_dim, self._output_dim, self._input_dim, self._output_dim)",""," def _evolve(self, state, qargs=None):"," return SuperOp(self)._evolve(state, qargs)",""," # ---------------------------------------------------------------------"," # BaseOperator methods"," # ---------------------------------------------------------------------",""," def conjugate(self):"," # Since conjugation is basis dependent we transform"," # to the Choi representation to compute the"," # conjugate channel"," return Chi(Choi(self).conjugate())",""," def transpose(self):"," return Chi(Choi(self).transpose())",""," def adjoint(self):"," return Chi(Choi(self).adjoint())",""," def compose(self, other: Chi, qargs: list | None = None, front: bool = False) -> Chi:"," 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