VQE

class VQE(estimator, ansatz, optimizer, *, gradient=None, initial_point=None, callback=None)

Bases: qiskit.algorithms.variational_algorithm.VariationalAlgorithm, qiskit.algorithms.minimum_eigensolvers.minimum_eigensolver.MinimumEigensolver

The variational quantum eigensolver (VQE) algorithm.

VQE is a hybrid quantum-classical algorithm that uses a variational technique to find the minimum eigenvalue of a given Hamiltonian operator $H$.

The VQE algorithm is executed using an estimator primitive, which computes expectation values of operators (observables).

An instance of VQE also requires an ansatz, a parameterized QuantumCircuit, to prepare the trial state $|\psi(\vec\theta)\rangle$. It also needs a classical optimizer which varies the circuit parameters $\vec\theta$ such that the expectation value of the operator on the corresponding state approaches a minimum,

The estimator is used to compute this expectation value for every optimization step.

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

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 one to use any SciPy minimizer, for instance as

from functools import partial
from scipy.optimize import minimize
 
optimizer = partial(minimize, method="L-BFGS-B")

The following attributes can be set via the initializer but can also be read and updated once the VQE object has been constructed.

estimator

ansatz

optimizer

gradient

callback

References

[1]: Peruzzo, A., et al, “A variational eigenvalue solver on a quantum processor”

arXiv:1304.3061

Parameters

• estimator (BaseEstimator) – The estimator primitive to compute the expectation value of the Hamiltonian operator.
• ansatz (QuantumCircuit) – A parameterized quantum circuit to prepare the trial state.
• optimizer (Optimizer |Minimizer) – A classical optimizer to find the minimum energy. This can either be a Qiskit Optimizer or a callable implementing the Minimizer protocol.
• gradient (BaseEstimatorGradient | None) – An optional estimator gradient to be used with the optimizer.
• initial_point (Sequence[float] | None) – An optional initial point (i.e. initial parameter values) for the optimizer. The length of the initial point must match the number of ansatz parameters. If None, a random point will be generated within certain parameter bounds. VQE will look to the ansatz for these bounds. If the ansatz does not specify bounds, bounds of $-2\pi$, $2\pi$ will be used.
• callback (Callable[[int, np.ndarray, float, dict[str, Any]], None] | None) – A callback that can access the intermediate data at each optimization step. These data are: the evaluation count, the optimizer parameters for the ansatz, the estimated value, and the metadata dictionary.

Methods

compute_minimum_eigenvalue

supports_aux_operators

Attributes

initial_point