Abstract

One of the most promising expected applications of near-term quantum computers lies in the study of static and dynamical properties of quantum many-body systems. Many quantum computing algorithms have been proposed with this goal in mind, with a focus on Hamiltonian eigenvalue extraction, a problem central to chemistry, physics, and materials science. However, the majority of established quantum algorithms require a prohibitively large number of resources for near-term hardware.

Here we describe the variational quantum phase estimation (VQPE) method, a compact and efficient real-time subspace algorithm to extract eigenvalues using quantum hardware. We theoretically and numerically explore a generalized Krylov scheme where the Krylov subspace is constructed through a parametrized real-time evolution, applicable to the VQPE algorithm as well as others. We discuss its application to fundamental problems in quantum computation such as electronic structure predictions for strongly correlated systems.