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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.","","\"\"\"","Superoperator representation of a Quantum Channel.\"\"\"","","from __future__ import annotations","","import copy","from typing import TYPE_CHECKING","","import numpy as np","","from qiskit.circuit.instruction import Instruction","from qiskit.circuit.quantumcircuit import QuantumCircuit","from qiskit.exceptions import QiskitError","from qiskit.quantum_info.operators.base_operator import BaseOperator","from qiskit.quantum_info.operators.channel.quantum_channel import QuantumChannel","from qiskit.quantum_info.operators.channel.transformations import _bipartite_tensor, _to_superop","from qiskit.quantum_info.operators.mixins import generate_apidocs","from qiskit.quantum_info.operators.op_shape import OpShape","from qiskit.quantum_info.operators.operator import Operator","","if TYPE_CHECKING:"," from qiskit.quantum_info.states.densitymatrix import DensityMatrix"," from qiskit.quantum_info.states.statevector import Statevector","","","class SuperOp(QuantumChannel):"," r\"\"\"Superoperator representation of a quantum channel.",""," The Superoperator representation of a quantum channel :math:`\\mathcal{E}`"," is a matrix :math:`S` such that the evolution of a"," :class:`~qiskit.quantum_info.DensityMatrix` :math:`\\rho` is given by",""," .. math::",""," |\\mathcal{E}(\\rho)\\rangle\\!\\rangle = S |\\rho\\rangle\\!\\rangle",""," where the double-ket notation :math:`|A\\rangle\\!\\rangle` denotes a vector"," formed by stacking the columns of the matrix :math:`A`"," *(column-vectorization)*.",""," 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: tuple | None = None,"," output_dims: tuple | None = None,"," ):"," \"\"\"Initialize a quantum channel Superoperator 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"," superoperator.",""," 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 Numpy array of shape (4**N, 4**N) qubit systems will be used. If"," the input operator is not an N-qubit operator, it will assign a"," single subsystem with dimension specified by the shape of the input."," \"\"\""," # If the input is a raw list or matrix we assume that it is"," # already a superoperator."," if isinstance(data, (list, np.ndarray)):"," # We initialize directly from superoperator matrix"," super_mat = np.asarray(data, dtype=complex)"," # Determine total input and output dimensions"," dout, din = super_mat.shape"," input_dim = int(np.sqrt(din))"," output_dim = int(np.sqrt(dout))"," if output_dim**2 != dout or input_dim**2 != din:"," raise QiskitError(\"Invalid shape for SuperOp matrix.\")"," 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"," # perform a simulation to construct the circuit superoperator."," # This will only work if the circuit or instruction can be"," # defined in terms of instructions which have no classical"," # register components. The instructions can be gates, reset,"," # or Kraus instructions. Any conditional gates or measure"," # will cause an exception to be raised."," data = self._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)"," # Now that the input is an operator we convert it to a"," # SuperOp object"," op_shape = data._op_shape"," input_dim, output_dim = data.dim"," rep = getattr(data, \"_channel_rep\", \"Operator\")"," super_mat = _to_superop(rep, data._data, input_dim, output_dim)"," # Initialize QuantumChannel"," super().__init__(super_mat, op_shape=op_shape)",""," def __array__(self, dtype=None):"," if dtype:"," return np.asarray(self.data, dtype=dtype)"," return self.data",""," @property"," def _tensor_shape(self):"," \"\"\"Return the tensor shape of the superoperator matrix\"\"\""," return 2 * tuple(reversed(self._op_shape.dims_l())) + 2 * tuple("," reversed(self._op_shape.dims_r())"," )",""," @property"," def _bipartite_shape(self):"," \"\"\"Return the shape for bipartite matrix\"\"\""," return (self._output_dim, self._output_dim, self._input_dim, self._input_dim)",""," # ---------------------------------------------------------------------"," # BaseOperator methods"," # ---------------------------------------------------------------------",""," def conjugate(self):"," ret = copy.copy(self)"," ret._data = np.conj(self._data)"," return ret",""," def transpose(self):"," ret = copy.copy(self)"," ret._data = np.transpose(self._data)"," ret._op_shape = self._op_shape.transpose()"," return ret",""," def adjoint(self):"," ret = copy.copy(self)"," ret._data = np.conj(np.transpose(self._data))"," ret._op_shape = self._op_shape.transpose()"," return ret",""," def tensor(self, other: SuperOp) -> SuperOp:"," if not isinstance(other, SuperOp):"," other = SuperOp(other)"," return self._tensor(self, other)",""," def expand(self, other: SuperOp) -> SuperOp:"," if not isinstance(other, SuperOp):"," other = SuperOp(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)"," ret._data = _bipartite_tensor("," a._data, b.data, shape1=a._bipartite_shape, shape2=b._bipartite_shape"," )"," return ret",""," def compose(self, other: SuperOp, qargs: list | None = None, front: bool = False) -> SuperOp:"," if qargs is None:"," qargs = getattr(other, \"qargs\", None)"," if not isinstance(other, SuperOp):"," other = SuperOp(other)"," # Validate dimensions are compatible and return the composed"," # operator dimensions"," new_shape = self._op_shape.compose(other._op_shape, qargs, front)"," input_dims = new_shape.dims_r()"," output_dims = new_shape.dims_l()",""," # Full composition of superoperators"," if qargs is None:"," if front:"," data = np.dot(self._data, other.data)"," else:"," data = np.dot(other.data, self._data)"," ret = SuperOp(data, input_dims, output_dims)"," ret._op_shape = new_shape"," return ret",""," # Compute tensor contraction indices from qargs"," num_qargs_l, num_qargs_r = self._op_shape.num_qargs"," if front:"," num_indices = num_qargs_r"," shift = 2 * num_qargs_l"," right_mul = True"," else:"," num_indices = num_qargs_l"," shift = 0"," right_mul = False",""," # Reshape current matrix"," # Note that we must reverse the subsystem dimension order as"," # qubit 0 corresponds to the right-most position in the tensor"," # product, which is the last tensor wire index."," tensor = np.reshape(self.data, self._tensor_shape)"," mat = np.reshape(other.data, other._tensor_shape)"," # Add first set of indices"," indices = [2 * num_indices - 1 - qubit for qubit in qargs] + ["," num_indices - 1 - qubit for qubit in qargs"," ]"," final_shape = [np.prod(output_dims) ** 2, np.prod(input_dims) ** 2]"," data = np.reshape("," Operator._einsum_matmul(tensor, mat, indices, shift, right_mul), final_shape"," )"," ret = SuperOp(data, input_dims, output_dims)"," ret._op_shape = new_shape"," return ret",""," # ---------------------------------------------------------------------"," # Additional methods"," # ---------------------------------------------------------------------",""," def _evolve(self, state, qargs=None):"," \"\"\"Evolve a quantum state by the quantum channel.",""," Args:"," state (DensityMatrix or Statevector): The input state."," qargs (list): a list of quantum state subsystem positions to apply"," the quantum channel on.",""," Returns:"," DensityMatrix: the output quantum state as a density matrix.",""," Raises:"," QiskitError: if the quantum channel dimension does not match the"," specified quantum state subsystem dimensions."," \"\"\""," # Prevent cyclic imports by importing DensityMatrix here"," # pylint: disable=cyclic-import"," from qiskit.quantum_info.states.densitymatrix import DensityMatrix",""," if not isinstance(state, DensityMatrix):"," state = DensityMatrix(state)",""," if qargs is None:"," # Evolution on full matrix"," if state._op_shape.shape[0] != self._op_shape.shape[1]:"," raise QiskitError("," \"Operator input dimension is not equal to density matrix dimension.\""," )"," # We reshape in column-major vectorization (Fortran order in Numpy)"," # since that is how the SuperOp is defined"," vec = np.ravel(state.data, order=\"F\")"," mat = np.reshape("," np.dot(self.data, vec), (self._output_dim, self._output_dim), order=\"F\""," )"," return DensityMatrix(mat, dims=self.output_dims())"," # Otherwise we are applying an operator only to subsystems"," # Check dimensions of subsystems match the operator"," if state.dims(qargs) != self.input_dims():"," raise QiskitError("," \"Operator input dimensions are not equal to statevector subsystem dimensions.\""," )"," # Reshape statevector and operator"," tensor = np.reshape(state.data, state._op_shape.tensor_shape)"," mat = np.reshape(self.data, self._tensor_shape)"," # Construct list of tensor indices of statevector to be contracted"," num_indices = len(state.dims())"," indices = [num_indices - 1 - qubit for qubit in qargs] + ["," 2 * num_indices - 1 - qubit for qubit in qargs"," ]"," tensor = Operator._einsum_matmul(tensor, mat, indices)"," # Replace evolved dimensions"," new_dims = list(state.dims())"," output_dims = self.output_dims()"," for i, qubit in enumerate(qargs):"," new_dims[qubit] = output_dims[i]"," new_dim = np.prod(new_dims)"," # reshape tensor to density matrix"," tensor = np.reshape(tensor, (new_dim, new_dim))"," return DensityMatrix(tensor, dims=new_dims)",""," @classmethod"," def _init_instruction(cls, instruction):"," \"\"\"Convert a QuantumCircuit or Instruction to a SuperOp.\"\"\""," # Convert circuit to an instruction"," if isinstance(instruction, QuantumCircuit):"," instruction = instruction.to_instruction()"," # Initialize an identity superoperator of the correct size"," # of the circuit"," op = SuperOp(np.eye(4**instruction.num_qubits))"," op._append_instruction(instruction)"," return op",""," @classmethod"," def _instruction_to_superop(cls, obj):"," \"\"\"Return superop for instruction if defined or None otherwise.\"\"\""," if not isinstance(obj, Instruction):"," raise QiskitError(\"Input is not an instruction.\")"," chan = None"," if obj.name == \"reset\":"," # For superoperator evolution we can simulate a reset as"," # a non-unitary superoperator matrix"," chan = SuperOp(np.array([[1, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]))"," if obj.name == \"kraus\":"," kraus = obj.params"," dim = len(kraus[0])"," chan = SuperOp(_to_superop(\"Kraus\", (kraus, None), dim, dim))"," elif hasattr(obj, \"to_matrix\"):"," # If instruction is a gate first we see if it has a"," # `to_matrix` definition and if so use that."," try:"," kraus = [obj.to_matrix()]"," dim = len(kraus[0])"," chan = SuperOp(_to_superop(\"Kraus\", (kraus, None), dim, dim))"," except QiskitError:"," pass"," return chan",""," def _append_instruction(self, obj, qargs=None):"," \"\"\"Update the current Operator by apply an instruction.\"\"\""," from qiskit.circuit.barrier import Barrier",""," chan = self._instruction_to_superop(obj)"," if chan is not None:"," # Perform the composition and inplace update the current state"," # of the operator"," op = self.compose(chan, qargs=qargs)"," self._data = op.data"," elif isinstance(obj, Barrier):"," return"," else:"," # If the instruction doesn't have a matrix defined we use its"," # circuit decomposition definition if it exists, otherwise we"," # cannot compose this gate and raise an error."," if obj.definition is None:"," raise QiskitError(f\"Cannot apply Instruction: {obj.name}\")"," if not isinstance(obj.definition, QuantumCircuit):"," raise QiskitError("," \"{} instruction definition is {}; \""," \"expected QuantumCircuit\".format(obj.name, type(obj.definition))"," )"," qubit_indices = {bit: idx for idx, bit in enumerate(obj.definition.qubits)}"," for instruction in obj.definition.data:"," if instruction.clbits:"," raise QiskitError("," \"Cannot 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