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qiskit.quantum_info.operators.channel.ptm의 소스 코드

# 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.

# pylint: disable=unpacking-non-sequence

"""
Pauli Transfer Matrix (PTM) 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.superop import SuperOp
from qiskit.quantum_info.operators.channel.transformations import _to_ptm


[문서]class PTM(QuantumChannel): r"""Pauli Transfer Matrix (PTM) representation of a Quantum Channel. The PTM representation of an :math:`n`-qubit quantum channel :math:`\mathcal{E}` is an :math:`n`-qubit :class:`SuperOp` :math:`R` defined with respect to vectorization in the Pauli basis instead of column-vectorization. The elements of the PTM :math:`R` are given by .. math:: R_{i,j} = \mbox{Tr}\left[P_i \mathcal{E}(P_j) \right] where :math:`[P_0, P_1, ..., P_{4^{n}-1}]` is the :math:`n`-qubit Pauli basis in lexicographic order. Evolution of a :class:`~qiskit.quantum_info.DensityMatrix` :math:`\rho` with respect to the PTM is given by .. math:: |\mathcal{E}(\rho)\rangle\!\rangle_P = S_P |\rho\rangle\!\rangle_P where :math:`|A\rangle\!\rangle_P` denotes vectorization in the Pauli basis :math:`\langle i | A\rangle\!\rangle_P = \mbox{Tr}[P_i A]`. 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] <https://arxiv.org/abs/1111.6950>`_ """
[문서] def __init__(self, data, input_dims=None, output_dims=None): """Initialize a PTM quantum channel 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 PTM. Additional Information: If the input or output dimensions are None, they will be automatically determined from the input data. The PTM 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)): # Should we force this to be real? ptm = np.asarray(data, dtype=complex) # Determine input and output dimensions dout, din = ptm.shape if input_dims: input_dim = np.product(input_dims) else: input_dim = int(np.sqrt(din)) if output_dims: output_dim = np.product(input_dims) else: output_dim = int(np.sqrt(dout)) if output_dim**2 != dout or input_dim**2 != din or input_dim != output_dim: raise QiskitError("Invalid shape for PTM 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 PTM object rep = getattr(data, '_channel_rep', 'Operator') ptm = _to_ptm(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 Pauli transfer 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__(ptm, input_dims, output_dims, 'PTM')
@property def _bipartite_shape(self): """Return the shape for bipartite matrix""" return (self._output_dim, self._output_dim, self._input_dim, self._input_dim)
[문서] def conjugate(self): """Return the conjugate of the QuantumChannel.""" # Since conjugation is basis dependent we transform # to the SuperOp representation to compute the # conjugate channel return PTM(SuperOp(self).conjugate())
[문서] def transpose(self): """Return the transpose of the QuantumChannel.""" # Since conjugation is basis dependent we transform # to the SuperOp representation to compute the # conjugate channel return PTM(SuperOp(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: PTM: 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 PTM( SuperOp(self).compose(other, qargs=qargs, front=front)) # Convert other to PTM if not isinstance(other, PTM): other = PTM(other) input_dims, output_dims = self._get_compose_dims(other, qargs, front) if front: data = np.dot(self._data, other.data) else: data = np.dot(other.data, self._data) return PTM(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: PTM: the matrix power of the SuperOp converted to a PTM 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 PTM(SuperOp(self).power(n))
[문서] def tensor(self, other): """Return the tensor product channel self ⊗ other. Args: other (QuantumChannel): a quantum channel. Returns: PTM: the tensor product channel self ⊗ other as a PTM object. Raises: QiskitError: if other cannot be converted to a channel. """ if not isinstance(other, PTM): other = PTM(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 PTM(data, input_dims, output_dims)
[문서] def expand(self, other): """Return the tensor product channel other ⊗ self. Args: other (QuantumChannel): a quantum channel. Returns: PTM: the tensor product channel other ⊗ self as a PTM object. Raises: QiskitError: if other cannot be converted to a channel. """ if not isinstance(other, PTM): other = PTM(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 PTM(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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