Source code for pennylane.qchem.observable_hf

# Copyright 2018-2022 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 functions needed for creating fermionic and qubit observables.
"""
# pylint: disable= too-many-branches, too-many-return-statements
import numpy as np
import pennylane as qml
from pennylane.fermi import FermiSentence, FermiWord
from pennylane.operation import active_new_opmath
from pennylane.pauli.utils import simplify


def fermionic_observable(constant, one=None, two=None, cutoff=1.0e-12):
    r"""Create a fermionic observable from molecular orbital integrals.

    Args:
        constant (array[float]): the contribution of the core orbitals and nuclei
        one (array[float]): the one-particle molecular orbital integrals
        two (array[float]): the two-particle molecular orbital integrals
        cutoff (float): cutoff value for discarding the negligible integrals

    Returns:
        FermiSentence: fermionic observable

    **Example**

    >>> constant = np.array([1.0])
    >>> integral = np.array([[0.5, -0.8270995], [-0.8270995, 0.5]])
    >>> fermionic_observable(constant, integral)
    1.0 * I
    + 0.5 * a⁺(0) a(0)
    + -0.8270995 * a⁺(0) a(2)
    + 0.5 * a⁺(1) a(1)
    + -0.8270995 * a⁺(1) a(3)
    + -0.8270995 * a⁺(2) a(0)
    + 0.5 * a⁺(2) a(2)
    + -0.8270995 * a⁺(3) a(1)
    + 0.5 * a⁺(3) a(3)
    """
    coeffs = qml.math.array([])

    if not qml.math.allclose(constant, 0.0):
        coeffs = qml.math.concatenate((coeffs, constant))
        operators = [[]]
    else:
        operators = []

    if one is not None:
        indices_one = qml.math.argwhere(abs(one) >= cutoff)
        # up-up + down-down terms
        operators_one = (indices_one * 2).tolist() + (indices_one * 2 + 1).tolist()
        coeffs_one = qml.math.tile(one[abs(one) >= cutoff], 2)
        coeffs = qml.math.convert_like(coeffs, one)
        coeffs = qml.math.concatenate((coeffs, coeffs_one))
        operators = operators + operators_one

    if two is not None:
        indices_two = np.array(qml.math.argwhere(abs(two) >= cutoff))
        n = len(indices_two)
        operators_two = (
            [(indices_two[i] * 2).tolist() for i in range(n)]  # up-up-up-up
            + [(indices_two[i] * 2 + [0, 1, 1, 0]).tolist() for i in range(n)]  # up-down-down-up
            + [(indices_two[i] * 2 + [1, 0, 0, 1]).tolist() for i in range(n)]  # down-up-up-down
            + [(indices_two[i] * 2 + 1).tolist() for i in range(n)]  # down-down-down-down
        )
        coeffs_two = qml.math.tile(two[abs(two) >= cutoff], 4) / 2

        coeffs = qml.math.concatenate((coeffs, coeffs_two))
        operators = operators + operators_two

    indices_sort = [operators.index(i) for i in sorted(operators)]
    if indices_sort:
        indices_sort = qml.math.array(indices_sort)

    sentence = FermiSentence({FermiWord({}): constant[0]})
    for c, o in zip(coeffs[indices_sort], sorted(operators)):
        if len(o) == 2:
            sentence.update({FermiWord({(0, o[0]): "+", (1, o[1]): "-"}): c})
        if len(o) == 4:
            sentence.update(
                {FermiWord({(0, o[0]): "+", (1, o[1]): "+", (2, o[2]): "-", (3, o[3]): "-"}): c}
            )
    sentence.simplify()

    return sentence


def qubit_observable(o_ferm, cutoff=1.0e-12):
    r"""Convert a fermionic observable to a PennyLane qubit observable.

    Args:
        o_ferm (Union[FermiWord, FermiSentence]): fermionic operator
        cutoff (float): cutoff value for discarding the negligible terms

    Returns:
        Operator: Simplified PennyLane Hamiltonian

    **Example**

    >>> w1 = qml.fermi.FermiWord({(0, 0) : '+', (1, 1) : '-'})
    >>> w2 = qml.fermi.FermiWord({(0, 1) : '+', (1, 2) : '-'})
    >>> s = qml.fermi.FermiSentence({w1 : 1.2, w2: 3.1})
    >>> print(qubit_observable(s))
      (-0.3j) [Y0 X1]
    + (0.3j) [X0 Y1]
    + (-0.775j) [Y1 X2]
    + (0.775j) [X1 Y2]
    + ((0.3+0j)) [Y0 Y1]
    + ((0.3+0j)) [X0 X1]
    + ((0.775+0j)) [Y1 Y2]
    + ((0.775+0j)) [X1 X2]

    If the new op-math is active, an arithmetic operator is returned.

    >>> qml.operation.enable_new_opmath()
    >>> w1 = qml.fermi.FermiWord({(0, 0) : '+', (1, 1) : '-'})
    >>> w2 = qml.fermi.FermiWord({(0, 0) : '+', (1, 1) : '-'})
    >>> s = qml.fermi.FermiSentence({w1 : 1.2, w2: 3.1})
    >>> print(qubit_observable(s))
    -0.775j * (Y(0) @ X(1)) + 0.775 * (Y(0) @ Y(1)) + 0.775 * (X(0) @ X(1)) + 0.775j * (X(0) @ Y(1))
    """
    h = qml.jordan_wigner(o_ferm, ps=True, tol=cutoff)
    h.simplify(tol=cutoff)

    if active_new_opmath():
        if not h.wires:
            return h.operation(wire_order=[0])
        return h.operation()

    if not h.wires:
        h = h.hamiltonian(wire_order=[0])
        return qml.Hamiltonian(
            h.coeffs, [qml.Identity(0) if o.name == "Identity" else o for o in h.ops]
        )

    h = h.hamiltonian()

    return simplify(
        qml.Hamiltonian(h.coeffs, [qml.Identity(0) if o.name == "Identity" else o for o in h.ops])
    )

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