# VQD¶

class VQD(ansatz=None, k=2, betas=None, optimizer=None, initial_point=None, gradient=None, expectation=None, include_custom=False, max_evals_grouped=1, callback=None, quantum_instance=None)[source]

Bases: qiskit.algorithms.variational_algorithm.VariationalAlgorithm, qiskit.algorithms.eigen_solvers.eigen_solver.Eigensolver

Pending deprecation: Variational Quantum Deflation algorithm.

The VQD class has been superseded by the qiskit.algorithms.eigensolvers.VQD class. This class will be deprecated in a future release and subsequently removed after that.

VQD is a quantum algorithm that uses a variational technique to find the k eigenvalues of the Hamiltonian $$H$$ of a given system.

The algorithm computes excited state energies of generalised hamiltonians by optimising over a modified cost function where each succesive eigen value is calculated iteratively by introducing an overlap term with all the previously computed eigenstaes that must be minimised, thus ensuring higher energy eigen states are found.

An instance of VQD requires defining three algorithmic sub-components: an integer k denoting the number of eigenstates to calculate, 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 values being measured of the input operator (Hamiltonian). The algorithm does this by iteratively refining each excited state to be orthogonal to all the previous excited states.

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.

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 VQD 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 VQD will default it to $$-2\pi$$; similarly, if the ansatz returns None as the upper bound, the default value will be $$2\pi$$.

Parameters
• ansatz (Optional[QuantumCircuit]) – A parameterized circuit used as ansatz for the wave function.

• k (int) – the number of eigenvalues to return. Returns the lowest k eigenvalues.

• betas (Optional[List[float]]) – beta parameters in the VQD paper. Should have length k - 1, with k the number of excited states. These hyperparameters balance the contribution of each overlap term to the cost function and have a default value computed as the mean square sum of the coefficients of the observable.

• optimizer (Union[Optimizer, Minimizer, 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 VQD 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. Only used to compute the ground state at the moment.

• 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 VQD 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 multiple points to compute the gradient can be passed and if computed in parallel 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 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, the evaluated standard deviation, and the current step.

• quantum_instance (Union[Backend, QuantumInstance, None]) – Quantum Instance or Backend

Methods

 compute_eigenvalues Computes eigenvalues. construct_circuit Return the circuits used to compute the expectation value. construct_expectation Generate the ansatz circuit and expectation value measurement, and return their runnable composition. get_energy_evaluation Returns a function handle to evaluates the energy at given parameters for the ansatz. print_settings Preparing the setting of VQD into a string. supports_aux_operators Whether computing the expectation value of auxiliary operators is supported.

Attributes

ansatz

Returns the ansatz.

Return type

QuantumCircuit

callback

Returns callback

Return type

Optional[Callable[[int, ndarray, float, float, int], None]]

expectation

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

Return type

Optional[ExpectationBase]

Return type

include_custom

Returns include_custom

Return type

bool

initial_point

Returns initial point.

Return type

Optional[ndarray]

max_evals_grouped

Returns max_evals_grouped

Return type

int

optimizer

Returns optimizer

Return type

Optimizer

quantum_instance

Returns quantum instance.

Return type

Optional[QuantumInstance]

setting

Prepare the setting of VQD as a string.