VQE

VQE(operator=None, var_form=None, optimizer=None, initial_point=None, expectation=None, include_custom=False, max_evals_grouped=1, aux_operators=None, callback=None, quantum_instance=None)

The Variational Quantum Eigensolver algorithm.

VQE(opens in a new tab) is a hybrid algorithm that uses a variational technique and interleaves quantum and classical computations in order to find the minimum eigenvalue of the Hamiltonian $H$ of a given system.

An instance of VQE requires defining two algorithmic sub-components: a trial state (ansatz) from Aqua’s variational_forms, and one of the classical optimizers. The ansatz is varied, via its set of parameters, by the optimizer, such that it works towards a state, as determined by the parameters applied to the variational form, that will result in the minimum expectation value being measured of the input operator (Hamiltonian).

An optional array of parameter values, via the initial_point, may be provided as the starting point for the search of the minimum eigenvalue. This feature is particularly useful such as when there are reasons to believe that the solution point is close to a particular point. As an example, when building the dissociation profile of a molecule, it is likely that using the previous computed optimal solution as the starting initial point for the next interatomic distance is going to reduce the number of iterations necessary for the variational algorithm to converge. Aqua provides an initial point tutorial(opens in a new tab) detailing this use case.

The length of the initial_point list value must match the number of the parameters expected by the variational form being used. If the initial_point is left at the default of None, then VQE will look to the variational form for a preferred value, based on its given initial state. If the variational form returns None, then a random point will be generated within the parameter bounds set, as per above. If the variational form provides None as the lower bound, then VQE will default it to $-2\pi$; similarly, if the variational form returns None as the upper bound, the default value will be $2\pi$.

Parameters

• operator (Union[OperatorBase, LegacyBaseOperator, None]) – Qubit operator of the Observable
• var_form (Union[QuantumCircuit, VariationalForm, None]) – A parameterized circuit used as Ansatz for the wave function.
• optimizer (Optional[Optimizer]) – A classical optimizer.
• initial_point (Optional[ndarray]) – An optional initial point (i.e. initial parameter values) for the optimizer. If None then VQE will look to the variational form for a preferred point and if not 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) 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.
• 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

backend

expectation

initial_point

operator

optimal_params

optimizer

quantum_instance

random

setting

var_form

Methods

cleanup_parameterized_circuits

compute_minimum_eigenvalue

construct_circuit

find_minimum

get_optimal_circuit

get_optimal_cost

get_optimal_vector

get_prob_vector_for_params

get_probabilities_for_counts

print_settings

run

set_backend

supports_aux_operators