# This code is part of a Qiskit project.
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# (C) Copyright IBM 2022, 2023.
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# This code is licensed under the Apache License, Version 2.0. You may
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"""The quantum approximate optimization algorithm."""
from __future__ import annotations
from typing import Callable, Any
import numpy as np
from qiskit.circuit import QuantumCircuit
from qiskit.circuit.library.n_local.qaoa_ansatz import QAOAAnsatz
from qiskit.quantum_info.operators.base_operator import BaseOperator
from qiskit.primitives import BaseSampler
from qiskit_algorithms.utils.validation import validate_min
from qiskit_algorithms.optimizers import Minimizer, Optimizer
from .sampling_vqe import SamplingVQE
[docs]class QAOA(SamplingVQE):
r"""
The Quantum Approximate Optimization Algorithm (QAOA).
QAOA is a well-known algorithm for finding approximate solutions to combinatorial-optimization
problems [1].
The QAOA implementation directly extends :class:`.SamplingVQE` and inherits its optimization
structure. However, unlike VQE, which can be configured with arbitrary ansatzes, QAOA uses its
own fine-tuned ansatz, which comprises :math:`p` parameterized global :math:`x` rotations and
:math:`p` different parameterizations of the problem hamiltonian. QAOA is thus principally
configured by the single integer parameter, ``reps``, which dictates the depth of the ansatz,
and thus affects the approximation quality.
An optional array of :math:`2p` parameter values, as the :attr:`initial_point`, may be provided
as the starting :math:`\beta` and :math:`\gamma` parameters for the QAOA ansatz [1].
An operator or a parameterized quantum circuit may optionally also be provided as a custom
:attr:`mixer` Hamiltonian. This allows in the case of quantum annealing [2] and QAOA [3], to run
constrained optimization problems where the mixer constrains the evolution to a feasible
subspace of the full Hilbert space.
The following attributes can be set via the initializer but can also be read and updated once
the QAOA object has been constructed.
Attributes:
sampler (BaseSampler): The sampler primitive to sample the circuits.
optimizer (Optimizer | Minimizer): A classical optimizer to find the minimum energy. This
can either be an :class:`.Optimizer` or a callable implementing the
:class:`.Minimizer` protocol.
reps (int): The integer parameter :math:`p`. Has a minimum valid value of 1.
initial_state: An optional initial state to prepend the QAOA circuit with.
mixer (QuantumCircuit | BaseOperator): The mixer Hamiltonian to evolve with or
a custom quantum circuit. Allows support of optimizations in constrained subspaces [2,
3] as well as warm-starting the optimization [4].
aggregation (float | Callable[[list[float]], float] | None): A float or callable to specify
how the objective function evaluated on the basis states should be aggregated. If a
float, this specifies the :math:`\alpha \in [0,1]` parameter for a CVaR expectation
value.
callback (Callable[[int, np.ndarray, float, dict[str, Any]], None] | None): A callback
that can access the intermediate data at each optimization step. These data are: the
evaluation count, the optimizer parameters for the ansatz, the evaluated value, and
the metadata dictionary.
References:
[1]: Farhi, E., Goldstone, J., Gutmann, S., "A Quantum Approximate Optimization Algorithm"
`arXiv:1411.4028 <https://arxiv.org/abs/1411.4028>`__
[2]: Hen, I., Spedalieri, F. M., "Quantum Annealing for Constrained Optimization"
`PhysRevApplied.5.034007 <https://doi.org/10.1103/PhysRevApplied.5.034007>`__
[3]: Hadfield, S. et al, "From the Quantum Approximate Optimization Algorithm to a Quantum
Alternating Operator Ansatz" `arXiv:1709.03489 <https://arxiv.org/abs/1709.03489>`__
[4]: Egger, D. J., Marecek, J., Woerner, S., "Warm-starting quantum optimization"
`arXiv: 2009.10095 <https://arxiv.org/abs/2009.10095>`__
"""
def __init__(
self,
sampler: BaseSampler,
optimizer: Optimizer | Minimizer,
*,
reps: int = 1,
initial_state: QuantumCircuit | None = None,
mixer: QuantumCircuit | BaseOperator = None,
initial_point: np.ndarray | None = None,
aggregation: float | Callable[[list[float]], float] | None = None,
callback: Callable[[int, np.ndarray, float, dict[str, Any]], None] | None = None,
) -> None:
r"""
Args:
sampler: The sampler primitive to sample the circuits.
optimizer: A classical optimizer to find the minimum energy. This can either be
an :class:`.Optimizer` or a callable implementing the :class:`.Minimizer`
protocol.
reps: The integer parameter :math:`p`. Has a minimum valid value of 1.
initial_state: An optional initial state to prepend the QAOA circuit with.
mixer: The mixer Hamiltonian to evolve with or a custom quantum circuit. Allows support
of optimizations in constrained subspaces [2, 3] as well as warm-starting the
optimization [4].
initial_point: An optional initial point (i.e. initial parameter values) for the
optimizer. The length of the initial point must match the number of :attr:`ansatz`
parameters. If ``None``, a random point will be generated within certain parameter
bounds. ``QAOA`` will look to the ansatz for these bounds. If the ansatz does not
specify bounds, bounds of :math:`-2\pi`, :math:`2\pi` will be used.
aggregation: A float or callable to specify how the objective function evaluated on the
basis states should be aggregated. If a float, this specifies the :math:`\alpha \in
[0,1]` parameter for a CVaR expectation value.
callback: A callback that can access the intermediate data at each optimization step.
These data are: the evaluation count, the optimizer parameters for the ansatz, the
evaluated value, the metadata dictionary.
"""
validate_min("reps", reps, 1)
self.reps = reps
self.mixer = mixer
self.initial_state = initial_state
self._cost_operator = None
super().__init__(
sampler=sampler,
ansatz=None,
optimizer=optimizer,
initial_point=initial_point,
aggregation=aggregation,
callback=callback,
)
def _check_operator_ansatz(self, operator: BaseOperator):
# Recreates a circuit based on operator parameter.
self.ansatz = QAOAAnsatz(
operator, self.reps, initial_state=self.initial_state, mixer_operator=self.mixer
).decompose() # TODO remove decompose once #6674 is fixed