Source code for pennylane.ops.functions.generator

# Copyright 2018-2021 Xanadu Quantum Technologies Inc.

# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at

#     http://www.apache.org/licenses/LICENSE-2.0

# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
This module contains the qml.generator function.
"""
# pylint: disable=protected-access
import inspect
import warnings

import numpy as np

import pennylane as qml
from pennylane.ops import LinearCombination, Prod, SProd, Sum


# pylint: disable=too-many-branches
def _generator_hamiltonian(gen, op):
    """Return the generator as type :class:`~ops.LinearCombination`."""

    if isinstance(gen, LinearCombination):
        return gen

    if isinstance(gen, (qml.Hermitian, qml.SparseHamiltonian)):
        if isinstance(gen, qml.Hermitian):
            mat = gen.parameters[0]

        elif isinstance(gen, qml.SparseHamiltonian):
            mat = gen.parameters[0].toarray()

        return qml.pauli_decompose(mat, wire_order=op.wires, hide_identity=True)

    if isinstance(gen, (SProd, Prod, Sum)):
        coeffs, ops = gen.terms()
        return qml.Hamiltonian(coeffs, ops)

    return qml.Hamiltonian([1.0], [gen])


# pylint: disable=no-member
def _generator_prefactor(gen):
    r"""Return the generator as ```(obs, prefactor)`` representing
    :math:`G=p \hat{O}`, where

    - prefactor :math:`p` is a float
    - observable `\hat{O}` is one of :class:`~.Hermitian`,
      :class:`~.SparseHamiltonian`, or a tensor product
      of Pauli words.
    """

    prefactor = 1.0

    gen = qml.simplify(gen) if isinstance(gen, Prod) else gen

    if isinstance(gen, LinearCombination):
        gen = qml.dot(gen.coeffs, gen.ops)  # convert to Sum

    if isinstance(gen, Prod):
        coeffs, ops = gen.terms()
        return ops[0], coeffs[0]

    if isinstance(gen, Sum):
        ops = [o.base if isinstance(o, SProd) else o for o in gen]
        coeffs = [o.scalar if isinstance(o, SProd) else 1 for o in gen]
        abs_coeffs = list(qml.math.abs(coeffs))
        if qml.math.allequal(coeffs[0], coeffs):
            # case where the Hamiltonian coefficients are all the same
            return qml.sum(*ops), coeffs[0]
        if qml.math.allequal(abs_coeffs[0], abs_coeffs):
            # absolute value of coefficients is the same
            prefactor = abs_coeffs[0]
            coeffs = [c / prefactor for c in coeffs]
            return qml.dot(coeffs, ops), prefactor

    elif isinstance(gen, SProd):
        return gen.base, gen.scalar

    return gen, prefactor


def _generator_backcompatibility(op):
    r"""Preserve backwards compatibility behaviour for PennyLane
    versions <=0.22, where generators returned List[type or ndarray, float].
    This function raises a deprecation warning, and converts to the new
    format where an instantiated Operator is returned."""
    warnings.warn(
        "The Operator.generator property is deprecated. Please update the operator so that "
        "\n\t1. Operator.generator() is a method, and"
        "\n\t2. Operator.generator() returns an Operator instance representing the operator.",
        qml.PennyLaneDeprecationWarning,
    )
    gen = op.generator

    if inspect.isclass(gen[0]):
        return gen[1] * gen[0](wires=op.wires)

    if isinstance(gen[0], np.ndarray) and len(gen[0].shape) == 2:
        return gen[1] * qml.Hermitian(gen[0], wires=op.wires)

    raise qml.operation.GeneratorUndefinedError


[docs]def generator(op: qml.operation.Operator, format="prefactor"):
    r"""Returns the generator of an operation.

    Args:
        op (.Operator or Callable): A single operator, or a function that
            applies a single quantum operation.
        format (str): The format to return the generator in. Must be one of ``'prefactor'``,
            ``'observable'``, or ``'hamiltonian'``. See below for more details.

    Returns:
        .Operator or tuple[.Observable, float]: The returned generator, with format/type
        dependent on the ``format`` argument.

        * ``"prefactor"``: Return the generator as ``(obs, prefactor)`` (representing
          :math:`G=p \hat{O}`), where:

          - observable :math:`\hat{O}` is one of :class:`~.Hermitian`,
            :class:`~.SparseHamiltonian`, or a tensor product
            of Pauli words.
          - prefactor :math:`p` is a float.

        * ``"observable"``: Return the generator as a single observable as directly defined
          by ``op``. Returned generators may be any type of observable, including
          :class:`~.Hermitian`, :class:`~.SparseHamiltonian`, or :class:`~.ops.LinearCombination`.

        * ``"hamiltonian"``: Similar to ``"observable"``, however the returned observable
          will always be converted into :class:`~.ops.LinearCombination` regardless of how ``op``
          encodes the generator.

        * ``"arithmetic"``: Similar to ``"hamiltonian"``, however the returned observable
          will always be converted into an arithmetic operator. The returned generator may be
          any type, including:
          :class:`~.ops.op_math.SProd`, :class:`~.ops.op_math.Prod`, :class:`~.ops.op_math.Sum`, or the operator itself.

    **Example**

    Given an operation, ``qml.generator`` returns the generator representation:

    >>> op = qml.CRX(0.6, wires=[0, 1])
    >>> qml.generator(op)
    (Projector([1], wires=[0]) @ X(1), -0.5)

    It can also be used in a functional form:

    >>> qml.generator(qml.CRX)(0.6, wires=[0, 1])
    (Projector([1], wires=[0]) @ X(1), -0.5)

    By default, ``generator`` will return the generator in the format of ``(obs, prefactor)``,
    corresponding to :math:`G=p \hat{O}`, where the observable :math:`\hat{O}` will
    always be given in tensor product form, or as a dense/sparse matrix.

    By using the ``format`` argument, the returned generator representation can
    be altered:

    >>> op = qml.RX(0.2, wires=0)
    >>> qml.generator(op, format="prefactor")  # output will always be (obs, prefactor)
    (X(0), -0.5)
    >>> qml.generator(op, format="hamiltonian")  # output will be a LinearCombination
    -0.5 * X(0)
    >>> qml.generator(qml.PhaseShift(0.1, wires=0), format="observable")  # ouput will be a simplified obs where possible
    Projector([1], wires=[0])
    >>> qml.generator(op, format="arithmetic")  # output is an instance of `SProd`
    -0.5 * X(0)
    """

    def processing_fn(*args, **kwargs):
        if callable(op):
            with qml.queuing.QueuingManager.stop_recording():
                gen_op = op(*args, **kwargs)
        else:
            gen_op = op

        if gen_op.num_params != 1:
            raise ValueError(
                f"Operation {gen_op.name} is not written in terms of a single parameter"
            )

        try:
            gen = gen_op.generator()
        except TypeError:
            # For backwards compatibility with PennyLane
            # versions <=0.22, assume gen_op.generator is a property
            gen = _generator_backcompatibility(gen_op)

        if not gen.is_hermitian:
            raise qml.QuantumFunctionError(
                f"Generator {gen.name} of operation {gen_op.name} is not hermitian"
            )

        if format == "prefactor":
            return _generator_prefactor(gen)

        if format == "hamiltonian":
            return _generator_hamiltonian(gen, gen_op)

        if format == "arithmetic":
            h = _generator_hamiltonian(gen, gen_op)
            return qml.dot(h.coeffs, h.ops)

        if format == "observable":
            return gen

        raise ValueError(
            "format must be one of ('prefactor', 'hamiltonian', 'observable', 'arithmetic')"
        )

    if callable(op):
        return processing_fn
    return processing_fn()