Theory of variational quantum simulation

• DOI: 10.22331/q-2019-10-07-191
• Publication Date: 2019-10-07T12:50:40Z
• Authors: Xiao Yuan; Suguru Endo; Qi Zhao; Ying Li; Simon C. Benjamin
• Keywords: Ansatz; Variational principle; Variational method

The variational method is a versatile tool for classical simulation of variety quantum systems. Great efforts have recently been devoted to its extension computing efficiently solving static many-body problems and simulating real imaginary time dynamics. In this work, we first review the conventional principles, including Rayleigh-Ritz problems, Dirac Frenkel principle, McLachlan's time-dependent We focus on dynamics discuss connections three principles. Previous works mainly unitary evolution pure states. introduce mixed states under general stochastic evolution. show how results can be reduced state case with correction term that takes accounts global phase alignment. For evolution, also extend it scenario Gibbs preparation. further elaborate design ansatz compatible post-selection measurement implementation generalised algorithms circuits. Our work completes theory applicable near-term hardware.