# QAOA¶

class QAOA(operator=None, optimizer=None, p=1, initial_state=None, mixer=None, initial_point=None, gradient=None, expectation=None, include_custom=False, max_evals_grouped=1, aux_operators=None, callback=None, quantum_instance=None)[source]

Bases: qiskit.aqua.algorithms.minimum_eigen_solvers.vqe.VQE

The Quantum Approximate Optimization Algorithm.

QAOA is a well-known algorithm for finding approximate solutions to combinatorial-optimization problems. The QAOA implementation in Aqua directly extends 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 $$p$$ parameterized global $$x$$ rotations and $$p$$ 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 $$2p$$ parameter values, as the initial_point, may be provided as the starting beta and gamma parameters (as identically named in the original QAOA paper) for the QAOA variational form.

An operator or a parameterized quantum circuit may optionally also be provided as a custom mixer Hamiltonian. This allows, as discussed in this paper for quantum annealing, and in this paper 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 initial_states may optionally be supplied.

Parameters
• operator (Union[OperatorBase, LegacyBaseOperator, None]) – Qubit operator

• optimizer (Optional[Optimizer]) – A classical optimizer.

• p (int) – the integer parameter p as specified in https://arxiv.org/abs/1411.4028, Has a minimum valid value of 1.

• initial_state (Union[QuantumCircuit, InitialState, None]) – An optional initial state to prepend the QAOA circuit with

• mixer (Union[QuantumCircuit, OperatorBase, LegacyBaseOperator, None]) – the mixer Hamiltonian to evolve with or a custom quantum circuit. Allows support of optimizations in constrained subspaces as per https://arxiv.org/abs/1709.03489 as well as warm-starting the optimization as introduced in http://arxiv.org/abs/2009.10095.

• initial_point (Optional[ndarray]) – An optional initial point (i.e. initial parameter values) for the optimizer. If None then it will simply compute a random one.

• gradient (Union[GradientBase, Callable[[Union[ndarray, List]], List], None]) – An optional gradient operator respectively a gradient function used for optimization.

• expectation (Optional[ExpectationBase]) – The Expectation converter for taking the average value of the Observable over the var_form state function. When None (the default) an 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 (bool) – When expectation parameter here is None setting this to True will allow the factory to include the custom Aer pauli expectation.

• max_evals_grouped (int) – 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[Union[OperatorBase, LegacyBaseOperator, None]]]) – 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 (Optional[Callable[[int, ndarray, float, float], None]]) – 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 (Union[QuantumInstance, Backend, BaseBackend, None]) – Quantum Instance or Backend

Methods

 cleanup_parameterized_circuits set parameterized circuits to None compute_minimum_eigenvalue Computes minimum eigenvalue. construct_circuit Return the circuits used to compute the expectation value. construct_expectation Generate the ansatz circuit and expectation value measurement, and return their runnable composition. find_minimum Optimize to find the minimum cost value. get_optimal_circuit Get the circuit with the optimal parameters. get_optimal_cost Get the minimal cost or energy found by the VQE. get_optimal_vector Get the simulation outcome of the optimal circuit. get_prob_vector_for_params Helper function to get probability vectors for a set of params get_probabilities_for_counts get probabilities for counts print_settings Preparing the setting of VQE into a string. run Execute the algorithm with selected backend. set_backend Sets backend with configuration. supports_aux_operators Whether computing the expectation value of auxiliary operators is supported.

Attributes

aux_operators

Returns aux operators

Return type

Optional[List[Optional[OperatorBase]]]

backend

Returns backend.

Return type

Union[Backend, BaseBackend]

expectation

The expectation value algorithm used to construct the expectation measurement from the observable.

Return type

ExpectationBase

initial_point

Returns initial point

Return type

Optional[ndarray]

initial_state

Returns: Returns the initial state.

Return type

Union[QuantumCircuit, InitialState, None]

mixer

Returns: Returns the mixer.

Return type

Union[QuantumCircuit, OperatorBase, LegacyBaseOperator]

operator

Returns operator

Return type

Optional[OperatorBase]

optimal_params

The optimal parameters for the variational form.

Return type

List[float]

optimizer

Returns optimizer

Return type

Optional[Optimizer]

quantum_instance

Returns quantum instance.

Return type

Optional[QuantumInstance]

random

Return a numpy random.

setting

Prepare the setting of VQE as a string.

var_form

Returns variational form

Return type

Union[QuantumCircuit, VariationalForm, None]