# qiskit.algorithms.QAOA¶

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)[Quellcode]

The Quantum Approximate Optimization Algorithm.

QAOA 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 $$p$$ 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 ansatz, 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 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 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.

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

• reps (int) – the integer parameter $$p$$ as specified in https://arxiv.org/abs/1411.4028, 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 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 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[QuantumInstance, BaseBackend, Backend, None]) – Quantum Instance or Backend

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

• reps (int) – the integer parameter $$p$$ as specified in https://arxiv.org/abs/1411.4028, 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 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 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[QuantumInstance, BaseBackend, Backend, None]) – Quantum Instance or Backend

Methods

 __init__([optimizer, reps, initial_state, …]) type optimizer Optional[Optimizer] set parameterized circuits to None compute_minimum_eigenvalue(operator[, …]) Computes minimum eigenvalue. construct_circuit(parameter, operator) Return the circuits used to compute the expectation value. construct_expectation(parameter, operator[, …]) Generate the ansatz circuit and expectation value measurement, and return their runnable composition. find_minimum([initial_point, ansatz, …]) Optimize to find the minimum cost value. get_energy_evaluation(operator[, …]) Returns a function handle to evaluates the energy at given parameters for the ansatz. Get the circuit with the optimal parameters. Get the minimal cost or energy found by the VQE. Get the simulation outcome of the optimal circuit. Helper function to get probability vectors for a set of params get probabilities for counts Preparing the setting of VQE into a string. Whether computing the expectation value of auxiliary operators is supported.

Attributes

 ansatz Returns the ansatz. expectation The expectation value algorithm used to construct the expectation measurement from the observable. gradient Returns the gradient. initial_point Returns initial point initial_state Returns: Returns the initial state. mixer Returns: Returns the mixer. optimal_params The optimal parameters for the ansatz. optimizer Returns optimizer quantum_instance Returns quantum instance. setting Prepare the setting of VQE as a string.
property ansatz

Returns the ansatz.

Rückgabetyp

Optional[QuantumCircuit]

cleanup_parameterized_circuits()

set parameterized circuits to None

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.

Parameter
• operator (OperatorBase) – Qubit operator of the Observable

• aux_operators (Optional[List[Optional[OperatorBase]]]) – 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.

Rückgabetyp

MinimumEigensolverResult

Rückgabe

MinimumEigensolverResult

construct_circuit(parameter, operator)

Return the circuits used to compute the expectation value.

Parameter
• parameter (Union[List[float], List[Parameter], ndarray]) – Parameters for the ansatz circuit.

• operator (OperatorBase) – Qubit operator of the Observable

Rückgabetyp

List[QuantumCircuit]

Rückgabe

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

construct_expectation(parameter, operator, return_expectation=False)

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

Parameter
• 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.

Rückgabetyp

Union[OperatorBase, Tuple[OperatorBase, ExpectationBase]]

Rückgabe

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

Verursacht
• AlgorithmError – If no operator has been provided.

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

property expectation

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

Rückgabetyp

Optional[ExpectationBase]

find_minimum(initial_point=None, ansatz=None, cost_fn=None, optimizer=None, gradient_fn=None)

Optimize to find the minimum cost value.

Parameter
• initial_point (Optional[ndarray]) – If not None will be used instead of any initial point supplied via constructor. If None and None was supplied to constructor then a random point will be used if the optimizer requires an initial point.

• ansatz (Optional[QuantumCircuit]) – If not None will be used instead of any ansatz supplied via constructor.

• cost_fn (Optional[Callable]) – If not None will be used instead of any cost_fn supplied via constructor.

• optimizer (Optional[Optimizer]) – If not None will be used instead of any optimizer supplied via constructor.

• gradient_fn (Optional[Callable]) – Optional gradient function for optimizer

Rückgabe

Optimized variational parameters, and corresponding minimum cost value.

Rückgabetyp

dict

Verursacht

ValueError – invalid input

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.

Parameter
• 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.

Rückgabetyp

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

Rückgabe

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

Verursacht

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

get_optimal_circuit()

Get the circuit with the optimal parameters.

Rückgabetyp

QuantumCircuit

get_optimal_cost()

Get the minimal cost or energy found by the VQE.

Rückgabetyp

float

get_optimal_vector()

Get the simulation outcome of the optimal circuit.

Rückgabetyp

Union[List[float], Dict[str, int]]

get_prob_vector_for_params(construct_circuit_fn, params_s, quantum_instance, construct_circuit_args=None)

Helper function to get probability vectors for a set of params

get_probabilities_for_counts(counts)

get probabilities for counts

property gradient

Rückgabetyp

Union[GradientBase, Callable, None]

property initial_point

Returns initial point

Rückgabetyp

Optional[ndarray]

property initial_state

Returns: Returns the initial state.

Rückgabetyp

Optional[QuantumCircuit]

property mixer

Returns: Returns the mixer.

Rückgabetyp

Union[QuantumCircuit, OperatorBase]

property optimal_params

The optimal parameters for the ansatz.

Rückgabetyp

ndarray

property optimizer

Returns optimizer

Rückgabetyp

Optional[Optimizer]

print_settings()

Preparing the setting of VQE into a string.

Rückgabe

the formatted setting of VQE

Rückgabetyp

str

property quantum_instance

Returns quantum instance.

Rückgabetyp

Optional[QuantumInstance]

property setting

Prepare the setting of VQE as a string.

classmethod 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.

Rückgabetyp

bool

Rückgabe

True if aux_operator expectations can be evaluated, False otherwise