VQE

class VQE(ansatz=None, optimizer=None, initial_point=None, gradient=None, expectation=None, include_custom=False, max_evals_grouped=1, callback=None, quantum_instance=None)

Bases: qiskit.algorithms.variational_algorithm.VariationalAlgorithm, qiskit.algorithms.minimum_eigen_solvers.minimum_eigen_solver.MinimumEigensolver

The Variational Quantum Eigensolver algorithm.

VQE is a quantum algorithm that uses a variational technique 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 (a.k.a. ansatz) which is a QuantumCircuit, 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 ansatz, 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. It 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 ansatz being used. If the initial_point is left at the default of None, then VQE will look to the ansatz for a preferred value, based on its given initial state. If the ansatz returns None, then a random point will be generated within the parameter bounds set, as per above. If the ansatz provides None as the lower bound, then VQE will default it to $-2\pi$; similarly, if the ansatz returns None as the upper bound, the default value will be $2\pi$.

The optimizer can either be one of Qiskit’s optimizers, such as SPSA or a callable with the following signature:

The above signature also allows to directly pass any SciPy minimizer, for instance as

Parameters

• ansatz (Optional[QuantumCircuit]) – A parameterized circuit used as Ansatz for the wave function.
• optimizer (Union[Optimizer, Callable[[Callable[[ndarray], float], ndarray, Optional[Callable[[ndarray], ndarray]], Optional[List[Tuple[float, float]]]], Union[OptimizeResult, OptimizerResult]], None]) – A classical optimizer. Can either be a Qiskit optimizer or a callable that takes an array as input and returns a Qiskit or SciPy optimization result.
• initial_point (Optional[ndarray]) – An optional initial point (i.e. initial parameter values) for the optimizer. If None then VQE will look to the ansatz 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 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. Deprecated 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

construct_circuit

construct_expectation

get_energy_evaluation

print_settings

supports_aux_operators

Attributes

ansatz

callback

expectation

gradient

include_custom

initial_point

max_evals_grouped

optimizer

quantum_instance

setting