# Quellcode fÃ¼r qiskit.quantum_info.operators.channel.ptm

# 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
# 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.

"""
Pauli Transfer Matrix (PTM) representation of a Quantum Channel.
"""

from __future__ import annotations
import copy
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
from qiskit.quantum_info.operators.mixins import generate_apidocs
from qiskit.quantum_info.operators.base_operator import BaseOperator

[Doku]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} = \frac{1}{2^n} \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 = \sqrt{\frac{1}{2^n}} \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>_ """ def __init__( self, data: QuantumCircuit | Instruction | BaseOperator | np.ndarray, input_dims: int | tuple | None = None, output_dims: int | tuple | None = 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.prod(input_dims) else: input_dim = int(np.sqrt(din)) if output_dims: output_dim = np.prod(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 or input_dim != output_dim: raise QiskitError("Input is not an n-qubit Pauli transfer matrix.") super().__init__(ptm, num_qubits=num_qubits) def __array__(self, dtype=None): if dtype: np.asarray(self.data, dtype=dtype) return self.data @property def _bipartite_shape(self): """Return the shape for bipartite matrix""" return (self._output_dim, self._output_dim, self._input_dim, self._input_dim) def _evolve(self, state, qargs=None): return SuperOp(self)._evolve(state, qargs) # --------------------------------------------------------------------- # BaseOperator methods # ---------------------------------------------------------------------
[Doku] def conjugate(self): # Since conjugation is basis dependent we transform # to the SuperOp representation to compute the # conjugate channel return PTM(SuperOp(self).conjugate())
[Doku] def transpose(self): return PTM(SuperOp(self).transpose())