Sample-based Krylov quantum diagonalization, theory, and applications.

We present recent theoretical and experimental results on sample-based Krylov quantum diagonalization (SKQD). SKQD provides a framework for attaining formally provably convergence for quantum simulation of ground state energies, provided the Hamiltonian, ground state, and initial reference state satisfy certain criteria similar to those of quantum phase estimation. Results of an SKQD experiment are variational and classically verifiable, providing a potential path to certifiable quantum advantage.