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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
# 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.

# pylint: disable=unpacking-non-sequence

Choi-matrix representation of a Quantum Channel.

import numpy as np

from qiskit.circuit.quantumcircuit import QuantumCircuit
from qiskit.circuit.instruction import Instruction
from qiskit.exceptions import QiskitError
from import QuantumChannel
from import SuperOp
from import _to_choi
from import _bipartite_tensor

[문서]class Choi(QuantumChannel): r"""Choi-matrix representation of a Quantum Channel. The Choi-matrix representation of a quantum channel :math:`\mathcal{E}` is a matrix .. math:: \Lambda = \sum_{i,j} |i\rangle\!\langle j|\otimes \mathcal{E}\left(|i\rangle\!\langle j|\right) Evolution of a :class:`~qiskit.quantum_info.DensityMatrix` :math:`\rho` with respect to the Choi-matrix is given by .. math:: \mathcal{E}(\rho) = \mbox{Tr}_{1}\left[\Lambda (\rho^T \otimes \mathbb{I})\right] where :math:`\mbox{Tr}_1` is the :func:`partial_trace` over subsystem 1. 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] <>`_ """
[문서] def __init__(self, data, input_dims=None, output_dims=None): """Initialize a quantum channel Choi 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 cannot be initialized as a Choi matrix. 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 Choi matrix. if isinstance(data, (list, np.ndarray)): # Initialize from raw numpy or list matrix. choi_mat = np.asarray(data, dtype=complex) # Determine input and output dimensions dim_l, dim_r = choi_mat.shape if dim_l != dim_r: raise QiskitError('Invalid Choi-matrix input.') if input_dims: input_dim = np.product(input_dims) if output_dims: output_dim = np.product(output_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 input Choi-matrix.") 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 Choi object rep = getattr(data, '_channel_rep', 'Operator') choi_mat = _to_choi(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 and format input and output dimensions input_dims = self._automatic_dims(input_dims, input_dim) output_dims = self._automatic_dims(output_dims, output_dim) super().__init__(choi_mat, input_dims, output_dims, 'Choi')
@property def _bipartite_shape(self): """Return the shape for bipartite matrix""" return (self._input_dim, self._output_dim, self._input_dim, self._output_dim)
[문서] def conjugate(self): """Return the conjugate of the QuantumChannel.""" return Choi(np.conj(self._data), self.input_dims(), self.output_dims())
[문서] def transpose(self): """Return the transpose of the QuantumChannel.""" # Make bipartite matrix d_in, d_out = self.dim data = np.reshape(self._data, (d_in, d_out, d_in, d_out)) # Swap input and output indices on bipartite matrix data = np.transpose(data, (1, 0, 3, 2)) # Transpose channel has input and output dimensions swapped data = np.reshape(data, (d_in * d_out, d_in * d_out)) return Choi(data, input_dims=self.output_dims(), output_dims=self.input_dims())
[문서] def compose(self, other, qargs=None, front=False): """Return the composed quantum channel self @ other. Args: other (QuantumChannel): a quantum channel. qargs (list or None): a list of subsystem positions to apply other on. If None apply on all subsystems [default: None]. front (bool): If True compose using right operator multiplication, instead of left multiplication [default: False]. Returns: Choi: The quantum channel self @ other. Raises: QiskitError: if other has incompatible dimensions. Additional Information: Composition (``@``) is defined as `left` matrix multiplication for :class:`SuperOp` matrices. That is that ``A @ B`` is equal to ``B * A``. Setting ``front=True`` returns `right` matrix multiplication ``A * B`` and is equivalent to the :meth:`dot` method. """ if qargs is None: qargs = getattr(other, 'qargs', None) if qargs is not None: return Choi( SuperOp(self).compose(other, qargs=qargs, front=front)) if not isinstance(other, Choi): other = Choi(other) input_dims, output_dims = self._get_compose_dims(other, qargs, front) input_dim = np.product(input_dims) output_dim = np.product(output_dims) if front: first = np.reshape(other._data, other._bipartite_shape) second = np.reshape(self._data, self._bipartite_shape) else: first = np.reshape(self._data, self._bipartite_shape) second = np.reshape(other._data, other._bipartite_shape) # Contract Choi matrices for composition data = np.reshape(np.einsum('iAjB,AkBl->ikjl', first, second), (input_dim * output_dim, input_dim * output_dim)) return Choi(data, input_dims, output_dims)
[문서] def power(self, n): """The matrix power of the channel. Args: n (int): compute the matrix power of the superoperator matrix. Returns: Choi: the matrix power of the SuperOp converted to a Choi channel. Raises: QiskitError: if the input and output dimensions of the QuantumChannel are not equal, or the power is not an integer. """ if n > 0: return super().power(n) return Choi(SuperOp(self).power(n))
[문서] def tensor(self, other): """Return the tensor product channel self ⊗ other. Args: other (QuantumChannel): a quantum channel. Returns: Choi: the tensor product channel self ⊗ other as a Choi object. Raises: QiskitError: if other cannot be converted to a channel. """ # Convert other to Choi if not isinstance(other, Choi): other = Choi(other) input_dims = other.input_dims() + self.input_dims() output_dims = other.output_dims() + self.output_dims() data = _bipartite_tensor(self._data,, shape1=self._bipartite_shape, shape2=other._bipartite_shape) return Choi(data, input_dims, output_dims)
[문서] def expand(self, other): """Return the tensor product channel other ⊗ self. Args: other (QuantumChannel): a quantum channel. Returns: Choi: the tensor product channel other ⊗ self as a Choi object. Raises: QiskitError: if other cannot be converted to a channel. """ # Convert other to Choi if not isinstance(other, Choi): other = Choi(other) input_dims = self.input_dims() + other.input_dims() output_dims = self.output_dims() + other.output_dims() data = _bipartite_tensor(, self._data, shape1=other._bipartite_shape, shape2=self._bipartite_shape) return Choi(data, input_dims, output_dims)
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. """ return SuperOp(self)._evolve(state, qargs)

© Copyright 2020, Qiskit Development Team. 최종 업데이트: 2021/01/17

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