부산대학교 도서관

In this work we present a detailed analysis of variational quantum phaseestimation (VQPE), a method based on real-time evolution for ground and excitedstate estimation on near-term hardware. We derive the theoretical ground onwhich the approach stands, and demonstrate that it provides one of the mostcompact variational expansions to date for solving strongly correlatedHamiltonians. At the center of VQPE lies a set of equations, with a simplegeometrical interpretation, which provides conditions for the time evolutiongrid in order to decouple eigenstates out of the set of time evolved expansionstates, and connects the method to the classical filter diagonalizationalgorithm. Further, we introduce what we call the unitary formulation of VQPE,in which the number of matrix elements that need to be measured scales linearlywith the number of expansion states, and we provide an analysis of the effectsof noise which substantially improves previous considerations. The unitaryformulation allows for a direct comparison to iterative phase estimation. Ourresults mark VQPE as both a natural and highly efficient quantum algorithm forground and excited state calculations of general many-body systems. Wedemonstrate a hardware implementation of VQPE for the transverse field Isingmodel. Further, we illustrate its power on a paradigmatic example of strongcorrelation (Cr2 in the SVP basis set), and show that it is possible to reachchemical accuracy with as few as ~50 timesteps.