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class QAOA(optimizer=None, reps=1, initial_state=None, mixer=None, initial_point=None, gradient=None, expectation=None, include_custom=False, max_evals_grouped=1, callback=None, quantum_instance=None)

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Bases: qiskit.algorithms.minimum_eigen_solvers.vqe.VQE

Pending deprecation: Quantum Approximate Optimization Algorithm.

The QAOA class has been superseded by the qiskit.algorithms.minimum_eigensolvers.QAOA class. This class will be deprecated in a future release and subsequently removed after that.

QAOA(opens in a new tab) is a well-known algorithm for finding approximate solutions to combinatorial-optimization problems.

The QAOA implementation directly extends VQE and inherits VQE’s optimization structure. However, unlike VQE, which can be configured with arbitrary ansatzes, QAOA uses its own fine-tuned ansatz, which comprises pp parameterized global xx rotations and pp different parameterizations of the problem hamiltonian. QAOA is thus principally configured by the single integer parameter, p, which dictates the depth of the ansatz, and thus affects the approximation quality.

An optional array of 2p2p parameter values, as the initial_point, may be provided as the starting beta and gamma parameters (as identically named in the original QAOA paper(opens in a new tab)) for the QAOA ansatz.

An operator or a parameterized quantum circuit may optionally also be provided as a custom mixer Hamiltonian. This allows, as discussed in this paper(opens in a new tab) for quantum annealing, and in this paper(opens in a new tab) for QAOA, to run constrained optimization problems where the mixer constrains the evolution to a feasible subspace of the full Hilbert space.


  • optimizer (Union[Optimizer, Minimizer, None]) – A classical optimizer, see also VQE for more details on the possible types.
  • reps (int) – the integer parameter pp as specified in in a new tab), Has a minimum valid value of 1.
  • initial_state (Optional[QuantumCircuit]) – An optional initial state to prepend the QAOA circuit with
  • mixer (Union[QuantumCircuit, OperatorBase, None]) – the mixer Hamiltonian to evolve with or a custom quantum circuit. Allows support of optimizations in constrained subspaces as per in a new tab) as well as warm-starting the optimization as introduced in in a new tab).
  • 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 ansatz 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.
  • 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 ansatz, the evaluated mean and the evaluated standard deviation.
  • quantum_instance (Union[Backend, QuantumInstance, None]) – Quantum Instance or Backend



QAOA.compute_minimum_eigenvalue(operator, aux_operators=None)

Computes minimum eigenvalue. Operator and aux_operators can be supplied here and if not None will override any already set into algorithm so it can be reused with different operators. While an operator is required by algorithms, aux_operators are optional. To ‘remove’ a previous aux_operators array use an empty list here.


  • operator (OperatorBase) – Qubit operator of the Observable
  • aux_operators (Union[List[Optional[OperatorBase]], Dict[str, OperatorBase], 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.

Return type





QAOA.construct_circuit(parameter, operator)

Return the circuits used to compute the expectation value.


  • parameter (Union[List[float], List[Parameter], ndarray]) – Parameters for the ansatz circuit.
  • operator (OperatorBase) – Qubit operator of the Observable

Return type



A list of the circuits used to compute the expectation value.


QAOA.construct_expectation(parameter, operator, return_expectation=False)

Generate the ansatz circuit and expectation value measurement, and return their runnable composition.


  • parameter (Union[List[float], List[Parameter], ndarray]) – Parameters for the ansatz circuit.
  • operator (OperatorBase) – Qubit operator of the Observable
  • return_expectation (bool) – If True, return the ExpectationBase expectation converter used in the construction of the expectation value. Useful e.g. to compute the standard deviation of the expectation value.

Return type

Union[OperatorBase, Tuple[OperatorBase, ExpectationBase]]


The Operator equalling the measurement of the ansatz StateFn by the Observable’s expectation StateFn, and, optionally, the expectation converter.


  • AlgorithmError – If no operator has been provided.
  • AlgorithmError – If no expectation is passed and None could be inferred via the ExpectationFactory.


QAOA.get_energy_evaluation(operator, return_expectation=False)

Returns a function handle to evaluates the energy at given parameters for the ansatz.

This is the objective function to be passed to the optimizer that is used for evaluation.


  • operator (OperatorBase) – The operator whose energy to evaluate.
  • return_expectation (bool) – If True, return the ExpectationBase expectation converter used in the construction of the expectation value. Useful e.g. to evaluate other operators with the same expectation value converter.

Return type

Callable[[ndarray], Union[float, List[float]]]


Energy of the hamiltonian of each parameter, and, optionally, the expectation converter.


RuntimeError – If the circuit is not parameterized (i.e. has 0 free parameters).


Preparing the setting of VQE into a string.


the formatted setting of VQE

Return type



classmethod QAOA.supports_aux_operators()

Whether computing the expectation value of auxiliary operators is supported.

If the minimum eigensolver computes an eigenstate of the main operator then it can compute the expectation value of the aux_operators for that state. Otherwise they will be ignored.

Return type



True if aux_operator expectations can be evaluated, False otherwise



Returns the ansatz.

Return type



Returns callback

Return type

Optional[Callable[[int, ndarray, float, float], None]]


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

Return type



Returns the gradient.

Return type

Union[GradientBase, Callable, None]


Returns include_custom

Return type



Returns initial point

Return type



Returns: Returns the initial state.

Return type



Returns max_evals_grouped

Return type



Returns: Returns the mixer.

Return type

Union[QuantumCircuit, OperatorBase]


Returns optimizer

Return type



Returns quantum instance.

Return type



Prepare the setting of VQE as a string.

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