VQE#

class VQE(estimator, ansatz, optimizer, *, gradient=None, initial_point=None, callback=None)[source]#

Bases: VariationalAlgorithm, 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,

\[\min_{\vec\theta} \langle\psi(\vec\theta)|H|\psi(\vec\theta)\rangle.\]

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#

The estimator primitive to compute the expectation value of the Hamiltonian operator.

Type:

BaseEstimator

ansatz#

A parameterized quantum circuit to prepare the trial state.

Type:

QuantumCircuit

optimizer#

A classical optimizer to find the minimum energy. This can either be a Qiskit Optimizer or a callable implementing the Minimizer protocol.

Type:

Optimizer | Minimizer

gradient#

An optional estimator gradient to be used with the optimizer.

Type:

BaseEstimatorGradient | None

callback#

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 evaluated mean, and the metadata dictionary.

Type:

Callable[[int, np.ndarray, float, dict[str, Any]], None] | None

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 (np.ndarray | 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.

Attributes

initial_point#

Methods

compute_minimum_eigenvalue(operator, aux_operators=None)[source]#

Computes the minimum eigenvalue. The operator and aux_operators are supplied here. While an operator is required by algorithms, aux_operators are optional.

Parameters:

  • operator (BaseOperator) – Qubit operator of the observable.

  • aux_operators (ListOrDict[BaseOperator] | None) – Optional list of auxiliary operators to be evaluated with the parameters of the minimum eigenvalue main result and their expectation values returned. For instance in chemistry these can be dipole operators and total particle count operators, so we can get values for these at the ground state.

Returns:

A minimum eigensolver result.

Return type:

VQEResult

classmethod supports_aux_operators()[source]#

Whether computing the expectation value of auxiliary operators is supported.

If the minimum eigensolver computes an eigenvalue of the main operator then it can compute the expectation value of the aux_operators for that state. Otherwise they will be ignored.

Returns:

True if aux_operator expectations can be evaluated, False otherwise

Return type:

bool