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qiskit.quantum_info.operators.channel.stinespring의 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.
"""
Stinespring representation of a Quantum Channel.
"""

import copy
from numbers import Number
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.predicates import is_identity_matrix
from qiskit.quantum_info.operators.channel.quantum_channel import QuantumChannel
from qiskit.quantum_info.operators.channel.kraus import Kraus
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_stinespring


[문서]class Stinespring(QuantumChannel): r"""Stinespring representation of a quantum channel. The Stinespring representation of a quantum channel :math:`\mathcal{E}` is a rectangular matrix :math:`A` such that the evolution of a :class:`~qiskit.quantum_info.DensityMatrix` :math:`\rho` is given by .. math:: \mathcal{E}(ρ) = \mbox{Tr}_2\left[A ρ A^\dagger\right] where :math:`\mbox{Tr}_2` is the :func:`partial_trace` over subsystem 2. A general operator map :math:`\mathcal{G}` can also be written using the generalized Stinespring representation which is given by two matrices :math:`A`, :math:`B` such that .. math:: \mathcal{G}(ρ) = \mbox{Tr}_2\left[A ρ B^\dagger\right] 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 quantum channel Stinespring 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 a list of Kraus matrices. Additional Information: If the input or output dimensions are None, they will be automatically determined from the input data. This can fail for the Stinespring operator if the output dimension cannot be automatically determined. """ # If the input is a list or tuple we assume it is a pair of general # Stinespring matrices. If it is a numpy array we assume that it is # a single Stinespring matrix. if isinstance(data, (list, tuple, np.ndarray)): if not isinstance(data, tuple): # Convert single Stinespring set to length 1 tuple stine = (np.asarray(data, dtype=complex), None) if isinstance(data, tuple) and len(data) == 2: if data[1] is None: stine = (np.asarray(data[0], dtype=complex), None) else: stine = (np.asarray(data[0], dtype=complex), np.asarray(data[1], dtype=complex)) dim_left, dim_right = stine[0].shape # If two Stinespring matrices check they are same shape if stine[1] is not None: if stine[1].shape != (dim_left, dim_right): raise QiskitError("Invalid Stinespring input.") input_dim = dim_right if output_dims: output_dim = np.product(output_dims) else: output_dim = input_dim if dim_left % output_dim != 0: raise QiskitError("Invalid output_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 # convert it to a SuperOp data = SuperOp._init_instruction(data) else: # We use the QuantumChannel init transform to intialize # other objects into a QuantumChannel or Operator object. data = self._init_transformer(data) data = self._init_transformer(data) input_dim, output_dim = data.dim # Now that the input is an operator we convert it to a # Stinespring operator rep = getattr(data, '_channel_rep', 'Operator') stine = _to_stinespring(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) # Initialize either single or general Stinespring if stine[1] is None or (stine[1] == stine[0]).all(): # Standard Stinespring map super().__init__((stine[0], None), input_dims=input_dims, output_dims=output_dims, channel_rep='Stinespring') else: # General (non-CPTP) Stinespring map super().__init__(stine, input_dims=input_dims, output_dims=output_dims, channel_rep='Stinespring')
@property def data(self): # Override to deal with data being either tuple or not if self._data[1] is None: return self._data[0] else: return self._data
[문서] def is_cptp(self, atol=None, rtol=None): """Return True if completely-positive trace-preserving.""" if atol is None: atol = self.atol if rtol is None: rtol = self.rtol if self._data[1] is not None: return False check = np.dot(np.transpose(np.conj(self._data[0])), self._data[0]) return is_identity_matrix(check, rtol=self.rtol, atol=self.atol)
[문서] def conjugate(self): """Return the conjugate of the QuantumChannel.""" # pylint: disable=assignment-from-no-return stine_l = np.conjugate(self._data[0]) stine_r = None if self._data[1] is not None: stine_r = np.conjugate(self._data[1]) return Stinespring((stine_l, stine_r), self.input_dims(), self.output_dims())
[문서] def transpose(self): """Return the transpose of the QuantumChannel.""" din, dout = self.dim dtr = self._data[0].shape[0] // dout stine = [None, None] for i, mat in enumerate(self._data): if mat is not None: stine[i] = np.reshape( np.transpose(np.reshape(mat, (dout, dtr, din)), (2, 1, 0)), (din * dtr, dout)) return Stinespring(tuple(stine), 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: Stinespring: The quantum channel self @ other. Raises: QiskitError: if other cannot be converted to a Stinespring or 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 Stinespring( SuperOp(self).compose(other, qargs=qargs, front=front)) # Otherwise we convert via Kraus representation rather than # superoperator to avoid unnecessary representation conversions return Stinespring(Kraus(self).compose(other, front=front))
[문서] def dot(self, other, qargs=None): """Return the right multiplied 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]. Returns: Stinespring: The quantum channel self * other. Raises: QiskitError: if other cannot be converted to a Stinespring or has incompatible dimensions. """ return super().dot(other, qargs=qargs)
[문서] def power(self, n): """The matrix power of the channel. Args: n (int): compute the matrix power of the superoperator matrix. Returns: Stinespring: the matrix power of the SuperOp converted to a Stinespring 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 Stinespring(SuperOp(self).power(n))
[문서] def tensor(self, other): """Return the tensor product channel self ⊗ other. Args: other (QuantumChannel): a quantum channel subclass. Returns: Stinespring: the tensor product channel other ⊗ self as a Stinespring object. Raises: QiskitError: if other cannot be converted to a channel. """ return self._tensor_product(other, reverse=False)
[문서] def expand(self, other): """Return the tensor product channel other ⊗ self. Args: other (QuantumChannel): a quantum channel subclass. Returns: Stinespring: the tensor product channel other ⊗ self as a Stinespring object. Raises: QiskitError: if other cannot be converted to a channel. """ return self._tensor_product(other, reverse=True)
def _add(self, other, qargs=None): """Return the QuantumChannel self + other. If ``qargs`` are specified the other operator will be added assuming it is identity on all other subsystems. Args: other (QuantumChannel): a quantum channel subclass. qargs (None or list): optional subsystems to add on (Default: None) Returns: Stinespring: the linear addition channel self + other. Raises: QiskitError: if other cannot be converted to a channel or has incompatible dimensions. """ # Since we cannot directly add two channels in the Stinespring # representation we convert to the Choi representation return Stinespring(Choi(self)._add(other, qargs=qargs)) def _multiply(self, other): """Return the QuantumChannel other * self. Args: other (complex): a complex number. Returns: Stinespring: the scalar multiplication other * self. Raises: QiskitError: if other is not a valid scalar. """ if not isinstance(other, Number): raise QiskitError("other is not a number") ret = copy.copy(self) # If the number is complex or negative we need to convert to # general Stinespring representation so we first convert to # the Choi representation if isinstance(other, complex) or other < 1: # Convert to Choi-matrix ret._data = Stinespring(Choi(self)._multiply(other))._data return ret # If the number is real we can update the Kraus operators # directly num = np.sqrt(other) stine_l, stine_r = self._data stine_l = num * self._data[0] stine_r = None if self._data[1] is not None: stine_r = num * self._data[1] ret._data = (stine_l, stine_r) return ret 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) def _tensor_product(self, other, reverse=False): """Return the tensor product channel. Args: other (QuantumChannel): a quantum channel subclass. reverse (bool): If False return self ⊗ other, if True return if True return (other ⊗ self) [Default: False] Returns: Stinespring: the tensor product channel as a Stinespring object. Raises: QiskitError: if other cannot be converted to a channel. """ # Convert other to Stinespring if not isinstance(other, Stinespring): other = Stinespring(other) # Tensor Stinespring ops sa_l, sa_r = self._data sb_l, sb_r = other._data # Reshuffle tensor dimensions din_a, dout_a = self.dim din_b, dout_b = other.dim dtr_a = sa_l.shape[0] // dout_a dtr_b = sb_l.shape[0] // dout_b if reverse: shape_in = (dout_b, dtr_b, dout_a, dtr_a, din_b * din_a) shape_out = (dout_b * dtr_b * dout_a * dtr_a, din_b * din_a) else: shape_in = (dout_a, dtr_a, dout_b, dtr_b, din_a * din_b) shape_out = (dout_a * dtr_a * dout_b * dtr_b, din_a * din_b) # Compute left Stinespring op if reverse: input_dims = self.input_dims() + other.input_dims() output_dims = self.output_dims() + other.output_dims() sab_l = np.kron(sb_l, sa_l) else: input_dims = other.input_dims() + self.input_dims() output_dims = other.output_dims() + self.output_dims() sab_l = np.kron(sa_l, sb_l) # Reravel indices sab_l = np.reshape( np.transpose(np.reshape(sab_l, shape_in), (0, 2, 1, 3, 4)), shape_out) # Compute right Stinespring op if sa_r is None and sb_r is None: sab_r = None else: if sa_r is None: sa_r = sa_l elif sb_r is None: sb_r = sb_l if reverse: sab_r = np.kron(sb_r, sa_r) else: sab_r = np.kron(sa_r, sb_r) # Reravel indices sab_r = np.reshape( np.transpose(np.reshape(sab_r, shape_in), (0, 2, 1, 3, 4)), shape_out) return Stinespring((sab_l, sab_r), input_dims, output_dims)

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

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