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 Hamiltonian, LinearCombination, SProd, Prod, Sum
from pennylane.operation import convert_to_H


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

    if isinstance(gen, (Hamiltonian, LinearCombination)):
        H = gen

    elif 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()

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

    elif isinstance(gen, qml.operation.Observable):
        H = qml.Hamiltonian([1.0], [gen])

    elif isinstance(gen, (SProd, Prod, Sum)):
        H = convert_to_H(gen)

    return H


# 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

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

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

    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:`~.Tensor`, :class:`~.SparseHamiltonian`, or :class:`~.Hamiltonian`. * ``"hamiltonian"``: Similar to ``"observable"``, however the returned observable will always be converted into :class:`~.Hamiltonian` 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 always be a Hamiltonian/LinearCombination -0.5 * X(0) >>> with qml.operation.disable_new_opmath_cm(): ... gen = qml.generator(op, format="hamiltonian")) # legacy Hamiltonian class ... print(gen, type(gen)) (-0.5) [X0] <class 'pennylane.ops.qubit.hamiltonian.Hamiltonian'> >>> 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()