numpy-minimum-eigensolver

Use NumPyMinimumEigensolver from qiskit_algorithms.minimum_eigensolvers and call compute_minimum_eigenvalue with a SparsePauliOp operator. It returns a result object with eigenvalue, eigenstate, and optional auxiliary operator evaluations.

NumPyEigensolver returns a list of all computed eigenvalues, while NumPyMinimumEigensolver delegates to it internally and returns only the single minimum eigenvalue and its eigenstate. The minimum solver also supports a filter_criterion for constrained selection.

Pass a callback filter_criterion(eigenstate, eigenvalue, aux_values) returning bool to the NumPyMinimumEigensolver constructor. Only eigenpairs passing the filter are eligible, and the minimum is selected among them; if none pass, the result eigenvalue is None.

Exact diagonalization builds a dense 2^n by 2^n matrix, so memory and runtime grow exponentially with qubit count. It is practical for roughly 10 to 12 qubits and should be used as a classical baseline rather than for large systems.

A None eigenvalue means the filter_criterion rejected every computed eigenpair, leaving no feasible state. Loosen the filter or set filter_criterion to None, and always check for None before using the result.