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

Subspace Diagonalization on Quantum Computers using Eigenvector Continuation