real_amplitudes.py

# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2020.
#
# 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.

"""The real-amplitudes 2-local circuit."""

from __future__ import annotations
from collections.abc import Callable, Iterable

import numpy as np

from qiskit.circuit import QuantumCircuit
from qiskit.circuit.library.standard_gates import RYGate, CXGate
from qiskit.utils.deprecation import deprecate_func
from .n_local import n_local, BlockEntanglement
from .two_local import TwoLocal


def real_amplitudes(
    num_qubits: int,
    entanglement: (
        BlockEntanglement
        | Iterable[BlockEntanglement]
        | Callable[[int], BlockEntanglement | Iterable[BlockEntanglement]]
    ) = "reverse_linear",
    reps: int = 3,
    skip_unentangled_qubits: bool = False,
    skip_final_rotation_layer: bool = False,
    parameter_prefix: str = "θ",
    insert_barriers: bool = False,
    name: str = "RealAmplitudes",
) -> QuantumCircuit:
    r"""Construct a real-amplitudes 2-local circuit.

    This circuit is a heuristic trial wave function used, e.g., as ansatz in chemistry, optimization
    or machine learning applications. The circuit consists of alternating layers of :math:`Y`
    rotations and :math:`CX` entanglements. The entanglement pattern can be user-defined or selected
    from a predefined set. This circuit is  "real amplitudes" since the prepared quantum states will
    only have real amplitudes.

    For example a ``real_amplitudes`` circuit with 2 repetitions on 3 qubits with ``"reverse_linear"``
    entanglement is

    .. parsed-literal::

         ┌──────────┐ ░            ░ ┌──────────┐ ░            ░ ┌──────────┐
         ┤ Ry(θ[0]) ├─░────────■───░─┤ Ry(θ[3]) ├─░────────■───░─┤ Ry(θ[6]) ├
         ├──────────┤ ░      ┌─┴─┐ ░ ├──────────┤ ░      ┌─┴─┐ ░ ├──────────┤
         ┤ Ry(θ[1]) ├─░───■──┤ X ├─░─┤ Ry(θ[4]) ├─░───■──┤ X ├─░─┤ Ry(θ[7]) ├
         ├──────────┤ ░ ┌─┴─┐└───┘ ░ ├──────────┤ ░ ┌─┴─┐└───┘ ░ ├──────────┤
         ┤ Ry(θ[2]) ├─░─┤ X ├──────░─┤ Ry(θ[5]) ├─░─┤ X ├──────░─┤ Ry(θ[8]) ├
         └──────────┘ ░ └───┘      ░ └──────────┘ ░ └───┘      ░ └──────────┘

    The entanglement can be set using the ``entanglement`` keyword as string or a list of
    index-pairs. See the documentation of :func:`.n_local`. Additional options that can be set include
    the number of repetitions, skipping rotation gates on qubits that are not entangled, leaving out
    the final rotation layer and inserting barriers in between the rotation and entanglement
    layers.

    Examples:

        .. plot::
           :include-source:
           :context:

           from qiskit.circuit.library import real_amplitudes

           ansatz = real_amplitudes(3, reps=2)  # create the circuit on 3 qubits
           ansatz.draw("mpl")

        .. plot::
           :include-source:
           :context:

           ansatz = real_amplitudes(3, entanglement="full", reps=2)  # it is the same unitary as above
           ansatz.draw("mpl")

        .. plot::
           :include-source:
           :context:

           ansatz = real_amplitudes(3, entanglement="linear", reps=2, insert_barriers=True)
           ansatz.draw("mpl")

        .. plot::
           :include-source:
           :context:

           ansatz = real_amplitudes(4, reps=2, entanglement=[[0,3], [0,2]], skip_unentangled_qubits=True)
           ansatz.draw("mpl")

    Args:
        num_qubits: The number of qubits of the RealAmplitudes circuit.
        reps: Specifies how often the structure of a rotation layer followed by an entanglement
            layer is repeated.
        entanglement: The indices specifying on which qubits the input blocks act.
            See :func:`.n_local` for detailed information.
        skip_final_rotation_layer: Whether a final rotation layer is added to the circuit.
        skip_unentangled_qubits: If ``True``, the rotation gates act only on qubits that
            are entangled. If ``False``, the rotation gates act on all qubits.
        parameter_prefix: The name of the free parameters.
        insert_barriers: If True, barriers are inserted in between each layer. If False,
            no barriers are inserted.
        name: The name of the circuit.

    Returns:
        A real-amplitudes circuit.
    """

    return n_local(
        num_qubits,
        ["ry"],
        ["cx"],
        entanglement,
        reps,
        insert_barriers,
        parameter_prefix,
        True,
        skip_final_rotation_layer,
        skip_unentangled_qubits,
        name,
    )


class RealAmplitudes(TwoLocal):
    r"""The real-amplitudes 2-local circuit.

    The ``RealAmplitudes`` circuit is a heuristic trial wave function used as Ansatz in chemistry
    applications or classification circuits in machine learning. The circuit consists of
    alternating layers of :math:`Y` rotations and :math:`CX` entanglements. The entanglement
    pattern can be user-defined or selected from a predefined set.
    It is called ``RealAmplitudes`` since the prepared quantum states will only have
    real amplitudes, the complex part is always 0.

    For example a ``RealAmplitudes`` circuit with 2 repetitions on 3 qubits with ``'reverse_linear'``
    entanglement is

    .. code-block:: text

         ┌──────────┐ ░            ░ ┌──────────┐ ░            ░ ┌──────────┐
         ┤ Ry(θ[0]) ├─░────────■───░─┤ Ry(θ[3]) ├─░────────■───░─┤ Ry(θ[6]) ├
         ├──────────┤ ░      ┌─┴─┐ ░ ├──────────┤ ░      ┌─┴─┐ ░ ├──────────┤
         ┤ Ry(θ[1]) ├─░───■──┤ X ├─░─┤ Ry(θ[4]) ├─░───■──┤ X ├─░─┤ Ry(θ[7]) ├
         ├──────────┤ ░ ┌─┴─┐└───┘ ░ ├──────────┤ ░ ┌─┴─┐└───┘ ░ ├──────────┤
         ┤ Ry(θ[2]) ├─░─┤ X ├──────░─┤ Ry(θ[5]) ├─░─┤ X ├──────░─┤ Ry(θ[8]) ├
         └──────────┘ ░ └───┘      ░ └──────────┘ ░ └───┘      ░ └──────────┘

    The entanglement can be set using the ``entanglement`` keyword as string or a list of
    index-pairs. See the documentation of :class:`~qiskit.circuit.library.TwoLocal` and
    :class:`~qiskit.circuit.NLocal` for more detail. Additional options that can be set include the
    number of repetitions, skipping rotation gates on qubits that are not entangled, leaving out
    the final rotation layer and inserting barriers in between the rotation and entanglement
    layers.

    If some qubits are not entangled with other qubits it makes sense to not apply rotation gates
    on these qubits, since a sequence of :math:`Y` rotations can be reduced to a single :math:`Y`
    rotation with summed rotation angles.

    Examples:

        >>> ansatz = RealAmplitudes(3, reps=2)  # create the circuit on 3 qubits
        >>> print(ansatz.decompose())
             ┌──────────┐                 ┌──────────┐                 ┌──────────┐
        q_0: ┤ Ry(θ[0]) ├──────────■──────┤ Ry(θ[3]) ├──────────■──────┤ Ry(θ[6]) ├
             ├──────────┤        ┌─┴─┐    ├──────────┤        ┌─┴─┐    ├──────────┤
        q_1: ┤ Ry(θ[1]) ├──■─────┤ X ├────┤ Ry(θ[4]) ├──■─────┤ X ├────┤ Ry(θ[7]) ├
             ├──────────┤┌─┴─┐┌──┴───┴───┐└──────────┘┌─┴─┐┌──┴───┴───┐└──────────┘
        q_2: ┤ Ry(θ[2]) ├┤ X ├┤ Ry(θ[5]) ├────────────┤ X ├┤ Ry(θ[8]) ├────────────
             └──────────┘└───┘└──────────┘            └───┘└──────────┘

        >>> ansatz = RealAmplitudes(3, entanglement='full', reps=2, flatten=True)
        >>> print(ansatz)
             ┌──────────┐          ┌──────────┐                      ┌──────────┐
        q_0: ┤ RY(θ[0]) ├──■────■──┤ RY(θ[3]) ├──────────────■────■──┤ RY(θ[6]) ├────────────
             ├──────────┤┌─┴─┐  │  └──────────┘┌──────────┐┌─┴─┐  │  └──────────┘┌──────────┐
        q_1: ┤ RY(θ[1]) ├┤ X ├──┼───────■──────┤ RY(θ[4]) ├┤ X ├──┼───────■──────┤ RY(θ[7]) ├
             ├──────────┤└───┘┌─┴─┐   ┌─┴─┐    ├──────────┤└───┘┌─┴─┐   ┌─┴─┐    ├──────────┤
        q_2: ┤ RY(θ[2]) ├─────┤ X ├───┤ X ├────┤ RY(θ[5]) ├─────┤ X ├───┤ X ├────┤ RY(θ[8]) ├
             └──────────┘     └───┘   └───┘    └──────────┘     └───┘   └───┘    └──────────┘

        >>> ansatz = RealAmplitudes(3, entanglement='linear', reps=2, insert_barriers=True,
        ... flatten=True)
        >>> qc = QuantumCircuit(3)  # create a circuit and append the RY variational form
        >>> qc.compose(ansatz, inplace=True)
        >>> qc.draw()
             ┌──────────┐ ░            ░ ┌──────────┐ ░            ░ ┌──────────┐
        q_0: ┤ RY(θ[0]) ├─░───■────────░─┤ RY(θ[3]) ├─░───■────────░─┤ RY(θ[6]) ├
             ├──────────┤ ░ ┌─┴─┐      ░ ├──────────┤ ░ ┌─┴─┐      ░ ├──────────┤
        q_1: ┤ RY(θ[1]) ├─░─┤ X ├──■───░─┤ RY(θ[4]) ├─░─┤ X ├──■───░─┤ RY(θ[7]) ├
             ├──────────┤ ░ └───┘┌─┴─┐ ░ ├──────────┤ ░ └───┘┌─┴─┐ ░ ├──────────┤
        q_2: ┤ RY(θ[2]) ├─░──────┤ X ├─░─┤ RY(θ[5]) ├─░──────┤ X ├─░─┤ RY(θ[8]) ├
             └──────────┘ ░      └───┘ ░ └──────────┘ ░      └───┘ ░ └──────────┘

        >>> ansatz = RealAmplitudes(4, reps=1, entanglement='circular', insert_barriers=True,
        ... flatten=True)
        >>> print(ansatz)
             ┌──────────┐ ░ ┌───┐                ░ ┌──────────┐
        q_0: ┤ RY(θ[0]) ├─░─┤ X ├──■─────────────░─┤ RY(θ[4]) ├
             ├──────────┤ ░ └─┬─┘┌─┴─┐           ░ ├──────────┤
        q_1: ┤ RY(θ[1]) ├─░───┼──┤ X ├──■────────░─┤ RY(θ[5]) ├
             ├──────────┤ ░   │  └───┘┌─┴─┐      ░ ├──────────┤
        q_2: ┤ RY(θ[2]) ├─░───┼───────┤ X ├──■───░─┤ RY(θ[6]) ├
             ├──────────┤ ░   │       └───┘┌─┴─┐ ░ ├──────────┤
        q_3: ┤ RY(θ[3]) ├─░───■────────────┤ X ├─░─┤ RY(θ[7]) ├
             └──────────┘ ░                └───┘ ░ └──────────┘

        >>> ansatz = RealAmplitudes(4, reps=2, entanglement=[[0,3], [0,2]],
        ... skip_unentangled_qubits=True, flatten=True)
        >>> print(ansatz)
             ┌──────────┐                 ┌──────────┐                 ┌──────────┐
        q_0: ┤ RY(θ[0]) ├──■───────■──────┤ RY(θ[3]) ├──■───────■──────┤ RY(θ[6]) ├
             └──────────┘  │       │      └──────────┘  │       │      └──────────┘
        q_1: ──────────────┼───────┼────────────────────┼───────┼──────────────────
             ┌──────────┐  │     ┌─┴─┐    ┌──────────┐  │     ┌─┴─┐    ┌──────────┐
        q_2: ┤ RY(θ[1]) ├──┼─────┤ X ├────┤ RY(θ[4]) ├──┼─────┤ X ├────┤ RY(θ[7]) ├
             ├──────────┤┌─┴─┐┌──┴───┴───┐└──────────┘┌─┴─┐┌──┴───┴───┐└──────────┘
        q_3: ┤ RY(θ[2]) ├┤ X ├┤ RY(θ[5]) ├────────────┤ X ├┤ RY(θ[8]) ├────────────
             └──────────┘└───┘└──────────┘            └───┘└──────────┘

    .. seealso::

        The :func:`.real_amplitudes` function constructs a functionally equivalent circuit, but faster.

    """

    @deprecate_func(
        since="1.3",
        additional_msg="Use the function qiskit.circuit.library.real_amplitudes instead.",
        pending=True,
    )
    def __init__(
        self,
        num_qubits: int | None = None,
        entanglement: str | list[list[int]] | Callable[[int], list[int]] = "reverse_linear",
        reps: int = 3,
        skip_unentangled_qubits: bool = False,
        skip_final_rotation_layer: bool = False,
        parameter_prefix: str = "θ",
        insert_barriers: bool = False,
        initial_state: QuantumCircuit | None = None,
        name: str = "RealAmplitudes",
        flatten: bool | None = None,
    ) -> None:
        """
        Args:
            num_qubits: The number of qubits of the RealAmplitudes circuit.
            reps: Specifies how often the structure of a rotation layer followed by an entanglement
                layer is repeated.
            entanglement: Specifies the entanglement structure. Can be a string ('full', 'linear'
                'reverse_linear, 'circular' or 'sca'), a list of integer-pairs specifying the indices
                of qubits entangled with one another, or a callable returning such a list provided with
                the index of the entanglement layer.
                Default to 'reverse_linear' entanglement.
                Note that 'reverse_linear' entanglement provides the same unitary as 'full'
                with fewer entangling gates.
                See the Examples section of :class:`~qiskit.circuit.library.TwoLocal` for more
                detail.
            initial_state: A `QuantumCircuit` object to prepend to the circuit.
            skip_unentangled_qubits: If True, the single qubit gates are only applied to qubits
                that are entangled with another qubit. If False, the single qubit gates are applied
                to each qubit in the Ansatz. Defaults to False.
            skip_final_rotation_layer: If False, a rotation layer is added at the end of the
                ansatz. If True, no rotation layer is added.
            parameter_prefix: The parameterized gates require a parameter to be defined, for which
                we use :class:`~qiskit.circuit.ParameterVector`.
            insert_barriers: If True, barriers are inserted in between each layer. If False,
                no barriers are inserted.
            flatten: Set this to ``True`` to output a flat circuit instead of nesting it inside multiple
                layers of gate objects. By default currently the contents of
                the output circuit will be wrapped in nested objects for
                cleaner visualization. However, if you're using this circuit
                for anything besides visualization its **strongly** recommended
                to set this flag to ``True`` to avoid a large performance
                overhead for parameter binding.
        """
        super().__init__(
            num_qubits=num_qubits,
            reps=reps,
            rotation_blocks=RYGate,
            entanglement_blocks=CXGate,
            entanglement=entanglement,
            initial_state=initial_state,
            skip_unentangled_qubits=skip_unentangled_qubits,
            skip_final_rotation_layer=skip_final_rotation_layer,
            parameter_prefix=parameter_prefix,
            insert_barriers=insert_barriers,
            name=name,
            flatten=flatten,
        )

    @property
    def parameter_bounds(self) -> list[tuple[float, float]]:
        """Return the parameter bounds.

        Returns:
            The parameter bounds.
        """
        return self.num_parameters * [(-np.pi, np.pi)]