  Quantum subspace diagonalization (QSD) methods are quantum-classical hybrid
methods, commonly used to find ground and excited state energies by projecting
the Hamiltonian to a smaller subspace. In applying these, the choice of
subspace basis is critical from the perspectives of basis completeness and
efficiency of implementation on quantum computers. In this work, we present
Eigenvector Continuation (EC) as a QSD method, where low-energy states of the
Hamiltonian at different points in parameter space are chosen as the subspace
basis. This unique choice enables rapid evaluation of low-energy spectra,
including ground and nearby excited states, with minimal hardware effort. As a
particular advantage, EC is able to capture the spectrum across ground state
crossovers corresponding to different symmetry sectors of the problem. We
demonstrate this method for interacting spin models and molecules.
