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# qiskit.quantum_info.operators.channel.chi의 소스 코드

# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2019.
#
# obtain a copy of this license in the LICENSE.txt file in the root directory
#
# 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

"""
Chi-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 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

[문서]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) = \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.

See reference  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] <https://arxiv.org/abs/1111.6950>_
"""

[문서]    def __init__(self, data, input_dims=None, output_dims=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.

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
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.product(input_dims)
if output_dims:
output_dim = np.product(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:
raise QiskitError("Input is not an n-qubit Chi matrix.")
# 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__(chi_mat, input_dims, output_dims, 'Chi')

@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."""
# Since conjugation is basis dependent we transform
# to the Choi representation to compute the
# conjugate channel
return Chi(Choi(self).conjugate())

[문서]    def transpose(self):
"""Return the transpose of the QuantumChannel."""
# Since conjugation is basis dependent we transform
# to the Choi representation to compute the
# conjugate channel
return Chi(Choi(self).transpose())

[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:
Chi: The quantum channel self @ other.

Raises:
QiskitError: if other has incompatible dimensions.

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 Chi(
SuperOp(self).compose(other, qargs=qargs, front=front))
# If no qargs we compose via Choi representation to avoid an additional
# representation conversion to SuperOp and then convert back to Chi
return Chi(Choi(self).compose(other, front=front))

[문서]    def power(self, n):
"""The matrix power of the channel.

Args:
n (int): compute the matrix power of the superoperator matrix.

Returns:
Chi: the matrix power of the SuperOp converted to a Chi 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 Chi(SuperOp(self).power(n))

[문서]    def tensor(self, other):
"""Return the tensor product channel self ⊗ other.

Args:
other (QuantumChannel): a quantum channel.

Returns:
Chi: the tensor product channel self ⊗ other as a Chi object.

Raises:
QiskitError: if other is not a QuantumChannel subclass.
"""
if not isinstance(other, Chi):
other = Chi(other)
input_dims = other.input_dims() + self.input_dims()
output_dims = other.output_dims() + self.output_dims()
data = np.kron(self._data, other.data)
return Chi(data, input_dims, output_dims)

[문서]    def expand(self, other):
"""Return the tensor product channel other ⊗ self.

Args:
other (QuantumChannel): a quantum channel.

Returns:
Chi: the tensor product channel other ⊗ self as a Chi object.

Raises:
QiskitError: if other is not a QuantumChannel subclass.
"""
if not isinstance(other, Chi):
other = Chi(other)
input_dims = self.input_dims() + other.input_dims()
output_dims = self.output_dims() + other.output_dims()
data = np.kron(other.data, self._data)
return Chi(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)