# Source code for qiskit.aqua.algorithms.minimum_eigen_solvers.qaoa.qaoa

```
# This code is part of Qiskit.
#
# (C) Copyright IBM 2018, 2020.
#
# 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 Quantum Approximate Optimization Algorithm. """
from typing import List, Callable, Optional, Union
import logging
import numpy as np
from qiskit.providers import BaseBackend
from qiskit.providers import Backend
from qiskit.aqua import QuantumInstance
from qiskit.aqua.operators import OperatorBase, ExpectationBase, LegacyBaseOperator
from qiskit.aqua.operators.gradients import GradientBase
from qiskit.aqua.components.initial_states import InitialState
from qiskit.aqua.components.optimizers import Optimizer
from qiskit.aqua.utils.validation import validate_min
from .var_form import QAOAVarForm
from ..vqe import VQE
logger = logging.getLogger(__name__)
# pylint: disable=invalid-name
# disable check for operator setter because of pylint bug
# pylint: disable=no-member
[docs]class QAOA(VQE):
"""
The Quantum Approximate Optimization Algorithm.
`QAOA <https://arxiv.org/abs/1411.4028>`__ is a well-known algorithm for finding approximate
solutions to combinatorial-optimization problems.
The QAOA implementation in Aqua directly extends :class:`VQE` and inherits VQE's
general hybrid optimization structure.
However, unlike VQE, which can be configured with arbitrary variational forms,
QAOA uses its own fine-tuned variational form, 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, *p*,
which dictates the depth of the variational form, and thus affects the approximation quality.
An optional array of :math:`2p` parameter values, as the *initial_point*, may be provided as the
starting **beta** and **gamma** parameters (as identically named in the
original `QAOA paper <https://arxiv.org/abs/1411.4028>`__) for the QAOA variational form.
An operator may optionally also be provided as a custom `mixer` Hamiltonian. This allows,
as discussed in `this paper <https://doi.org/10.1103/PhysRevApplied.5.034007>`__
for quantum annealing, and in `this paper <https://arxiv.org/abs/1709.03489>`__ for QAOA,
to run constrained optimization problems where the mixer constrains
the evolution to a feasible subspace of the full Hilbert space.
An initial state from Aqua's :mod:`~qiskit.aqua.components.initial_states` may optionally
be supplied.
"""
[docs] def __init__(self,
operator: Union[OperatorBase, LegacyBaseOperator] = None,
optimizer: Optimizer = None,
p: int = 1,
initial_state: Optional[InitialState] = None,
mixer: Union[OperatorBase, LegacyBaseOperator] = None,
initial_point: Optional[np.ndarray] = None,
gradient: Optional[Union[GradientBase, Callable[[Union[np.ndarray, List]],
List]]] = None,
expectation: Optional[ExpectationBase] = None,
include_custom: bool = False,
max_evals_grouped: int = 1,
aux_operators: Optional[List[Optional[Union[OperatorBase, LegacyBaseOperator]]]] =
None,
callback: Optional[Callable[[int, np.ndarray, float, float], None]] = None,
quantum_instance: Optional[
Union[QuantumInstance, BaseBackend, Backend]] = None) -> None:
"""
Args:
operator: Qubit operator
optimizer: A classical optimizer.
p: the integer parameter p as specified in https://arxiv.org/abs/1411.4028,
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. Allows support of optimizations in
constrained subspaces as per https://arxiv.org/abs/1709.03489
initial_point: An optional initial point (i.e. initial parameter values)
for the optimizer. If ``None`` then it will simply compute a random one.
gradient: An optional gradient operator respectively a gradient function used for
optimization.
expectation: The Expectation converter for taking the average value of the
Observable over the var_form state function. When None (the default) an
:class:`~qiskit.aqua.operators.expectations.ExpectationFactory` is used to select
an appropriate expectation based on the operator and backend. When using Aer
qasm_simulator backend, with paulis, it is however much faster to leverage custom
Aer function for the computation but, although VQE performs much faster
with it, the outcome is ideal, with no shot noise, like using a state vector
simulator. If you are just looking for the quickest performance when choosing Aer
qasm_simulator and the lack of shot noise is not an issue then set `include_custom`
parameter here to True (defaults to False).
include_custom: When `expectation` parameter here is None setting this to True will
allow the factory to include the custom Aer pauli expectation.
max_evals_grouped: Max number of evaluations performed simultaneously. Signals the
given optimizer that more than one set of parameters can be supplied so that
potentially the expectation values can be computed in parallel. Typically this is
possible when a finite difference gradient is used by the optimizer such that
multiple points to compute the gradient can be passed and if computed in parallel
improve overall execution time. Ignored if a gradient operator or function is
given.
aux_operators: Optional list of auxiliary operators to be evaluated with the eigenstate
of the minimum eigenvalue main result and their expectation values returned.
For instance in chemistry these can be dipole operators, total particle count
operators so we can get values for these at the ground state.
callback: a callback that can access the intermediate data during the optimization.
Four parameter values are passed to the callback as follows during each evaluation
by the optimizer for its current set of parameters as it works towards the minimum.
These are: the evaluation count, the optimizer parameters for the
variational form, the evaluated mean and the evaluated standard deviation.
quantum_instance: Quantum Instance or Backend
"""
validate_min('p', p, 1)
self._p = p
self._mixer_operator = mixer.to_opflow() if isinstance(mixer, LegacyBaseOperator) else mixer
self._initial_state = initial_state
# VQE will use the operator setter, during its constructor, which is overridden below and
# will cause the var form to be built
super().__init__(operator,
None,
optimizer,
initial_point=initial_point,
gradient=gradient,
expectation=expectation,
include_custom=include_custom,
max_evals_grouped=max_evals_grouped,
callback=callback,
quantum_instance=quantum_instance,
aux_operators=aux_operators)
@VQE.operator.setter # type: ignore
def operator(self, operator: Union[OperatorBase, LegacyBaseOperator]) -> None:
""" Sets operator """
# Need to wipe the var_form in case number of qubits differs from operator.
self.var_form = None
# Setting with VQE's operator property
super(QAOA, self.__class__).operator.__set__(self, operator) # type: ignore
self.var_form = QAOAVarForm(self.operator,
self._p,
initial_state=self._initial_state,
mixer_operator=self._mixer_operator)
```