lie_trotter.py

# This code is part of Qiskit.
#
# (C) Copyright IBM 2021.
#
# 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 Lie-Trotter product formula."""

from __future__ import annotations

import inspect
from collections.abc import Callable
from typing import Any
import numpy as np
from qiskit.circuit.quantumcircuit import QuantumCircuit
from qiskit.quantum_info.operators import SparsePauliOp, Pauli
from qiskit.utils.deprecation import deprecate_arg

from .product_formula import ProductFormula


class LieTrotter(ProductFormula):
    r"""The Lie-Trotter product formula.

    The Lie-Trotter formula approximates the exponential of two non-commuting operators
    with products of their exponentials up to a second order error:

    .. math::

        e^{A + B} \approx e^{A}e^{B}.

    In this implementation, the operators are provided as sum terms of a Pauli operator.
    For example, we approximate

    .. math::

        e^{-it(XX + ZZ)} = e^{-it XX}e^{-it ZZ} + \mathcal{O}(t^2).

    References:

        [1]: D. Berry, G. Ahokas, R. Cleve and B. Sanders,
        "Efficient quantum algorithms for simulating sparse Hamiltonians" (2006).
        `arXiv:quant-ph/0508139 <https://arxiv.org/abs/quant-ph/0508139>`_
        [2]: N. Hatano and M. Suzuki,
        "Finding Exponential Product Formulas of Higher Orders" (2005).
        `arXiv:math-ph/0506007 <https://arxiv.org/pdf/math-ph/0506007.pdf>`_
    """

    @deprecate_arg(
        name="atomic_evolution",
        since="1.2",
        predicate=lambda callable: callable is not None
        and len(inspect.signature(callable).parameters) == 2,
        deprecation_description=(
            "The 'Callable[[Pauli | SparsePauliOp, float], QuantumCircuit]' signature of the "
            "'atomic_evolution' argument"
        ),
        additional_msg=(
            "Instead you should update your 'atomic_evolution' function to be of the following "
            "type: 'Callable[[QuantumCircuit, Pauli | SparsePauliOp, float], None]'."
        ),
        pending=True,
    )
    def __init__(
        self,
        reps: int = 1,
        insert_barriers: bool = False,
        cx_structure: str = "chain",
        atomic_evolution: (
            Callable[[Pauli | SparsePauliOp, float], QuantumCircuit]
            | Callable[[QuantumCircuit, Pauli | SparsePauliOp, float], None]
            | None
        ) = None,
        wrap: bool = False,
    ) -> None:
        """
        Args:
            reps: The number of time steps.
            insert_barriers: Whether to insert barriers between the atomic evolutions.
            cx_structure: How to arrange the CX gates for the Pauli evolutions, can be
                ``"chain"``, where next neighbor connections are used, or ``"fountain"``,
                where all qubits are connected to one. This only takes effect when
                ``atomic_evolution is None``.
            atomic_evolution: A function to apply the evolution of a single :class:`.Pauli`, or
                :class:`.SparsePauliOp` of only commuting terms, to a circuit. The function takes in
                three arguments: the circuit to append the evolution to, the Pauli operator to
                evolve, and the evolution time. By default, a single Pauli evolution is decomposed
                into a chain of ``CX`` gates and a single ``RZ`` gate.
                Alternatively, the function can also take Pauli operator and evolution time as
                inputs and returns the circuit that will be appended to the overall circuit being
                built.
            wrap: Whether to wrap the atomic evolutions into custom gate objects. This only takes
                effect when ``atomic_evolution is None``.
        """
        super().__init__(1, reps, insert_barriers, cx_structure, atomic_evolution, wrap)

    def synthesize(self, evolution):
        # get operators and time to evolve
        operators = evolution.operator
        time = evolution.time

        # construct the evolution circuit
        single_rep = QuantumCircuit(operators[0].num_qubits)

        if not isinstance(operators, list):
            pauli_list = [(Pauli(op), np.real(coeff)) for op, coeff in operators.to_list()]
        else:
            pauli_list = [(op, 1) for op in operators]

        for i, (op, coeff) in enumerate(pauli_list):
            self.atomic_evolution(single_rep, op, coeff * time / self.reps)
            if self.insert_barriers and i != len(pauli_list) - 1:
                single_rep.barrier()

        return single_rep.repeat(self.reps, insert_barriers=self.insert_barriers).decompose()

    @property
    def settings(self) -> dict[str, Any]:
        """Return the settings in a dictionary, which can be used to reconstruct the object.

        Returns:
            A dictionary containing the settings of this product formula.

        Raises:
            NotImplementedError: If a custom atomic evolution is set, which cannot be serialized.
        """
        if self._atomic_evolution is not None:
            raise NotImplementedError(
                "Cannot serialize a product formula with a custom atomic evolution."
            )

        return {
            "reps": self.reps,
            "insert_barriers": self.insert_barriers,
            "cx_structure": self._cx_structure,
            "wrap": self._wrap,
        }