VQE
class qiskit.algorithms.minimum_eigensolvers.VQE(estimator, ansatz, optimizer, *, gradient=None, initial_point=None, callback=None)
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 .
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 . It also needs a classical optimizer
which varies the circuit parameters 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
The estimator primitive to compute the expectation value of the Hamiltonian operator.
Type
ansatz
optimizer
A classical optimizer to find the minimum energy. This can either be a Qiskit Optimizer
or a callable implementing the Minimizer
protocol.
Type
gradient
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”
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 theMinimizer
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. IfNone
, 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 , 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
compute_minimum_eigenvalue(operator, aux_operators=None)
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 | PauliSumOp) – Qubit operator of the observable.
- aux_operators (ListOrDict[BaseOperator | PauliSumOp] | 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
supports_aux_operators
classmethod supports_aux_operators()
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