- 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)¶
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
Noneas the lower bound, then VQE will default it to \(-2\pi\); similarly, if the ansatz returns
Noneas the upper bound, the default value will be \(2\pi\).
The optimizer can either be one of Qiskit’s optimizers, such as
SPSAor a callable with the following signature:
The callable _must_ have the argument names
fun, x0, jac, boundsas indicated in the following code block.
from qiskit.algorithms.optimizers import OptimizerResult def my_minimizer(fun, x0, jac=None, bounds=None) -> OptimizerResult: # Note that the callable *must* have these argument names! # Args: # fun (callable): the function to minimize # x0 (np.ndarray): the initial point for the optimization # jac (callable, optional): the gradient of the objective function # bounds (list, optional): a list of tuples specifying the parameter bounds result = OptimizerResult() result.x = # optimal parameters result.fun = # optimal function value return result
The above signature also allows to directly pass any SciPy minimizer, for instance as
from functools import partial from scipy.optimize import minimize optimizer = partial(minimize, method="L-BFGS-B")
QuantumCircuit]) – A parameterized circuit used as Ansatz for the wave function.
ndarray]) – An optional initial point (i.e. initial parameter values) for the optimizer. If
Nonethen VQE will look to the ansatz for a preferred point and if not will simply compute a random one.
None]) – An optional gradient function or operator for optimizer.
ExpectationBase]) – The Expectation converter for taking the average value of the Observable over the ansatz state function. When
None(the default) an
ExpectationFactoryis 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
bool) – When expectation parameter here is None setting this to
Truewill allow the factory to include the custom Aer pauli expectation.
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.
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.`
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.
Returns a function handle to evaluates the energy at given parameters for the ansatz.
Preparing the setting of VQE into a string.
Whether computing the expectation value of auxiliary operators is supported.
The expectation value algorithm used to construct the expectation measurement from the observable.
Returns initial point
Prepare the setting of VQE as a string.