numyeigensolver

Use NumPyEigensolver from qiskit_algorithms.eigensolvers with a BaseOperator such as SparsePauliOp. Call compute_eigenvalues(operator) with k set to the number of eigenvalues you want, and read result.eigenvalues and result.eigenstates.

NumPyEigensolver is a classical exact eigensolver that diagonalizes a qubit operator using NumPy and SciPy. It serves as a reference baseline for benchmarking quantum eigensolvers like VQE, with no quantum circuit construction involved.

Pass a filter_criterion callable with signature filter_criterion(eigenstate, eigenvalue, aux_values) returning a boolean. Only eigenpairs passing the predicate are returned, so the result may contain fewer than k entries.

The dense matrix scales as 2^n by 2^n, so memory grows exponentially. Around 10-12 qubits is the practical dense limit (about 128 MB complex128 at n=12); beyond that, dense diagonalization may exhaust memory.

Complex eigenvalues appear when the input operator is not Hermitian. In that case the solver uses numpy.linalg.eig or scipy.sparse.linalg.eigs instead of the Hermitian eigh/eigsh paths, and sorting is by real part.