Source code for povm_toolbox.quantum_info.multi_qubit_dual

# (C) Copyright IBM 2024.
#
# 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.

"""MultiQubitDual."""

from __future__ import annotations

import sys

if sys.version_info < (3, 12):
    from typing_extensions import override
else:
    from typing import override  # pragma: no cover

import numpy as np
from qiskit.quantum_info import Operator

from povm_toolbox.utilities import double_ket_to_matrix

from .base import BaseDual, BaseFrame
from .multi_qubit_frame import MultiQubitFrame




class MultiQubitDual(MultiQubitFrame, BaseDual):
    """Class that collects all information that any Dual over multiple qubits should specify.

    This is a representation of a dual frame. Its elements are specified as a list of
    :class:`~qiskit.quantum_info.Operator`.
    """



    @override
    def is_dual_to(self, frame: BaseFrame) -> bool:
        if isinstance(frame, MultiQubitFrame):
            return np.allclose(frame @ np.conj(self).T, np.eye(self.dimension**2), atol=1e-6)
        raise NotImplementedError




    @override
    @classmethod
    def build_dual_from_frame(
        cls, frame: BaseFrame, alphas: tuple[float, ...] | None = None
    ) -> MultiQubitDual:
        if isinstance(frame, MultiQubitFrame):
            # Set default values for alphas if none is provided.
            if alphas is None:
                alphas = tuple(np.real(np.trace(frame_op.data)) for frame_op in frame.operators)
            # Check that the number of alpha-parameters match the number of operators
            # forming the ``frame``.
            elif len(alphas) != frame.num_operators:
                raise ValueError(
                    f"The number of alpha-parameters should be equal to the number of"
                    f" operators in the frame ({frame.num_operators}). Here, {len(alphas)}"
                    " parameters were provided."
                )

            # Set the weighting matrix according to the alpha-parameters
            diag_trace = np.diag([1.0 / alpha for alpha in alphas])
            # Compute the weighed frame super-operator.
            superop = frame @ diag_trace @ np.conj(frame).T

            # Solve the linear system to find the dual operators.
            dual_operators_array = np.linalg.solve(
                superop,
                frame @ diag_trace,
            )
            # Convert dual operators from double-ket to operator representation.
            dual_operators = [Operator(double_ket_to_matrix(op)) for op in dual_operators_array.T]

            return cls(dual_operators)

        # We could build a ``MultiQubitDual`` instance (i.e. joint dual frame) that
        # is a dual frame to a ``ProductFrame``, but we have not implemented this yet.
        raise NotImplementedError(f"Not implemented for {type(frame)}")