class VQE(operator=None, var_form=None, optimizer=None, initial_point=None, gradient=None, expectation=None, include_custom=False, max_evals_grouped=1, aux_operators=None, callback=None, quantum_instance=None)[source]

The Variational Quantum Eigensolver algorithm.

VQE 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 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 \(2\pi\).


The VQE stores the parameters of var_form sorted by name to map the values provided by the optimizer to the circuit. This is done to ensure reproducible results, for example such that running the optimization twice with same random seeds yields the same result. Also, the optimal_point of the result object can be used as initial point of another VQE run by passing it as initial_point to the initializer.

  • 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.

  • gradient (Union[GradientBase, Callable, None]) – An optional gradient function or operator for optimizer.

  • 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. Deprecated if a gradient operator or function is given.

  • 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, Backend, BaseBackend, None]) – Quantum Instance or Backend



Returns aux operators


Returns backend.


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


Returns initial point


Returns operator


The optimal parameters for the variational form.


Returns optimizer


Returns quantum instance.


Return a numpy random.


Prepare the setting of VQE as a string.


Returns variational form



set parameterized circuits to None

VQE.compute_minimum_eigenvalue([operator, …])

Computes minimum eigenvalue.


Return the circuits used to compute the expectation value.


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

VQE.find_minimum([initial_point, var_form, …])

Optimize to find the minimum cost value.


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.

VQE.get_prob_vector_for_params(…[, …])

Helper function to get probability vectors for a set of params


get probabilities for counts


Preparing the setting of VQE into a string.


Execute the algorithm with selected backend.

VQE.set_backend(backend, **kwargs)

Sets backend with configuration.


Whether computing the expectation value of auxiliary operators is supported.