QAOA
class QAOA(operator=None, optimizer=None, p=1, initial_state=None, mixer=None, initial_point=None, expectation=None, include_custom=False, max_evals_grouped=1, aux_operators=None, callback=None, quantum_instance=None)
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 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 variational form, 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 variational form.
An operator 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 (
Optional[InitialState]) – An optional initial state to prepend the QAOA circuit with - mixer (
Union[OperatorBase,LegacyBaseOperator,None]) – the mixer Hamiltonian to evolve with. Allows support of optimizations in constrained subspaces as per https://arxiv.org/abs/1709.03489 - initial_point (
Optional[ndarray]) – An optional initial point (i.e. initial parameter values) for the optimizer. IfNonethen it will simply compute a random one. - expectation (
Optional[ExpectationBase]) – The Expectation converter for taking the average value of the Observable over the var_form 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. - 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,BaseBackend,None]) – Quantum Instance or Backend
Attributes
aux_operators
Type: Optional[List[Optional[qiskit.aqua.operators.operator_base.OperatorBase]]]
Returns aux operators
Return type
Optional[List[Optional[OperatorBase]]]
backend
expectation
Type: qiskit.aqua.operators.expectations.expectation_base.ExpectationBase
The expectation value algorithm used to construct the expectation measurement from the observable.
Return type
initial_point
Type: Optional[numpy.ndarray]
Returns initial point
Return type
Optional[ndarray]
operator
Type: Optional[qiskit.aqua.operators.operator_base.OperatorBase]
Returns operator
Return type
Optional[OperatorBase]
optimal_params
Type: List[float]
The optimal parameters for the variational form.
Return type
List[float]
optimizer
Type: Optional[qiskit.aqua.components.optimizers.optimizer.Optimizer]
Returns optimizer
Return type
Optional[Optimizer]
quantum_instance
Type: Union[None, qiskit.aqua.quantum_instance.QuantumInstance]
Returns quantum instance.
Return type
Optional[QuantumInstance]
random
Return a numpy random.
setting
Prepare the setting of VQE as a string.
var_form
Type: Optional[Union[qiskit.circuit.quantumcircuit.QuantumCircuit, qiskit.aqua.components.variational_forms.variational_form.VariationalForm]]
Returns variational form
Return type
Union[QuantumCircuit, VariationalForm, None]
Methods
cleanup_parameterized_circuits
QAOA.cleanup_parameterized_circuits()
set parameterized circuits to None
compute_minimum_eigenvalue
QAOA.compute_minimum_eigenvalue(operator=None, 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 (
Union[OperatorBase,LegacyBaseOperator,None]) – If not None replaces operator in algorithm - aux_operators (
Optional[List[Union[OperatorBase,LegacyBaseOperator,None]]]) – If not None replaces aux_operators in algorithm
Return type
Returns
MinimumEigensolverResult
construct_circuit
QAOA.construct_circuit(parameter)
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.
Return type
Returns
The Operator equalling the measurement of the ansatz StateFn by the Observable’s expectation StateFn.
Raises
AquaError – If no operator has been provided.
find_minimum
QAOA.find_minimum(initial_point=None, var_form=None, cost_fn=None, optimizer=None, gradient_fn=None)
Optimize to find the minimum cost value.
Parameters
- 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. - var_form (
Union[QuantumCircuit,VariationalForm,None]) – If not None will be used instead of any variational form 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
Returns
Optimized variational parameters, and corresponding minimum cost value.
Return type
dict
Raises
ValueError – invalid input
get_optimal_circuit
get_optimal_cost
QAOA.get_optimal_cost()
Get the minimal cost or energy found by the VQE.
Return type
float
get_optimal_vector
QAOA.get_optimal_vector()
Get the simulation outcome of the optimal circuit.
Return type
Union[List[float], Dict[str, int]]
get_prob_vector_for_params
QAOA.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
QAOA.get_probabilities_for_counts(counts)
get probabilities for counts
print_settings
QAOA.print_settings()
Preparing the setting of VQE into a string.
Returns
the formatted setting of VQE
Return type
str
run
QAOA.run(quantum_instance=None, **kwargs)
Execute the algorithm with selected backend.
Parameters
- quantum_instance (
Union[QuantumInstance,BaseBackend,None]) – the experimental setting. - kwargs (dict) – kwargs
Returns
results of an algorithm.
Return type
dict
Raises
AquaError – If a quantum instance or backend has not been provided
set_backend
QAOA.set_backend(backend, **kwargs)
Sets backend with configuration.
Return type
None
supports_aux_operators
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