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)
Bases: qiskit.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 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 parameterized global rotations and 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 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.
Parameters
- optimizer (
Union[Optimizer,Callable[[Callable[[ndarray],float],ndarray,Optional[Callable[[ndarray],ndarray]],Optional[List[Tuple[float,float]]]],Union[OptimizeResult,OptimizerResult]],None]) – A classical optimizer, see alsoVQEfor more details on the possible types. - reps (
int) – the integer parameter 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. IfNonethen 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) anExpectationFactoryis 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,Backend,BaseBackend,None]) – Quantum Instance or Backend
Methods
compute_minimum_eigenvalue
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.
Parameters
- 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
MinimumEigensolverResult
Returns
MinimumEigensolverResult
construct_circuit
QAOA.construct_circuit(parameter, operator)
Return the circuits used to compute the expectation value.
Parameters
- parameter (
Union[List[float],List[Parameter],ndarray]) – Parameters for the ansatz circuit. - operator (
OperatorBase) – Qubit operator of the Observable
Return type
List[QuantumCircuit]
Returns
A list of the circuits used to compute the expectation value.
construct_expectation
QAOA.construct_expectation(parameter, operator, return_expectation=False)
Generate the ansatz circuit and expectation value measurement, and return their runnable composition.
Parameters
- 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 theExpectationBaseexpectation 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]]
Returns
The Operator equalling the measurement of the ansatz StateFn by the Observable’s expectation StateFn, and, optionally, the expectation converter.
Raises
- AlgorithmError – If no operator has been provided.
- AlgorithmError – If no expectation is passed and None could be inferred via the ExpectationFactory.
get_energy_evaluation
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.
Parameters
- operator (
OperatorBase) – The operator whose energy to evaluate. - return_expectation (
bool) – If True, return theExpectationBaseexpectation 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]]]
Returns
Energy of the hamiltonian of each parameter, and, optionally, the expectation converter.
Raises
RuntimeError – If the circuit is not parameterized (i.e. has 0 free parameters).
print_settings
QAOA.print_settings()
Preparing the setting of VQE into a string.
Returns
the formatted setting of VQE
Return type
str
supports_aux_operators
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
bool
Returns
True if aux_operator expectations can be evaluated, False otherwise
Attributes
ansatz
Returns the ansatz.
Return type
QuantumCircuit
callback
Returns callback
Return type
Optional[Callable[[int, ndarray, float, float], None]]
expectation
The expectation value algorithm used to construct the expectation measurement from the observable.
Return type
Optional[ExpectationBase]
gradient
Returns the gradient.
Return type
Union[GradientBase, Callable, None]
include_custom
Returns include_custom
Return type
bool
initial_point
Returns initial point
Return type
Optional[ndarray]
initial_state
Returns: Returns the initial state.
Return type
Optional[QuantumCircuit]
max_evals_grouped
Returns max_evals_grouped
Return type
int
mixer
Returns: Returns the mixer.
Return type
Union[QuantumCircuit, OperatorBase]
optimizer
Returns optimizer
Return type
Optimizer
quantum_instance
Returns quantum instance.
Return type
Optional[QuantumInstance]
setting
Prepare the setting of VQE as a string.