Title: Real-Time Evolution for Ultracompact Hamiltonian Eigenstates on Quantum Hardware

Abstract

Here we present a detailed analysis of variational quantum phase estimation (VQPE), a method based on real-time evolution for ground- and excited-state estimation on near-term hardware. We derive the theoretical ground on which the approach stands, and demonstrate that it provides one of the most compact variational expansions to date for solving strongly correlated Hamiltonians, when starting from an appropriate reference state. At the center of VQPE lies a set of equations, with a simple geometrical interpretation, which provides conditions for the time evolution grid in order to decouple eigenstates out of the set of time-evolved expansion states, and connects the method to the classical filter-diagonalization algorithm. Furthermore, we introduce what we call the unitary formulation of VQPE, in which the number of matrix elements that need to be measured scales linearly with the number of expansion states, and we provide an analysis of the effects of noise that substantially improves previous considerations. The unitary formulation allows for a direct comparison to iterative phase estimation. Our results mark VQPE as both a natural and highly efficient quantum algorithm for ground- and excited-state calculations of general many-body systems. We demonstrate a hardware implementation of VQPE for the transverse field Ising model.more » Furthermore, we illustrate its power on a paradigmatic example of strong correlation (Cr₂ in the def2-SVP basis set), and show that it is possible to reach chemical accuracy with as few as approximately 50 time steps.« less

Authors:

Klymko, Katherine; Mejuto-Zaera, Carlos ;

• Search DOE PAGES for author "Mejuto-Zaera, Carlos"
• Search DOE PAGES for ORCID "0000-0001-5921-0959"

Cotton, Stephen J. ;

• Search DOE PAGES for author "Cotton, Stephen J."
• Search DOE PAGES for ORCID "0000-0001-8716-5817"

Wudarski, Filip ;

• Search DOE PAGES for author "Wudarski, Filip"
• Search DOE PAGES for ORCID "0000-0002-0911-8342"

Urbanek, Miroslav; Hait, Diptarka ;

• Search DOE PAGES for author "Hait, Diptarka"
• Search DOE PAGES for ORCID "0000-0003-1570-920X"

Head-Gordon, Martin; Whaley, K. Birgitta; Moussa, Jonathan; Wiebe, Nathan; de Jong, Wibe A.; Tubman, Norm M.

Publication Date:

Tue May 03 00:00:00 EDT 2022

Research Org.:

Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

Sponsoring Org.:

USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division; NASA Ames Research Center; US Air Force Office of Scientific Research (AFOSR); NASA Academic Mission Services; Google Quantum AI

OSTI Identifier:

1866278

Alternate Identifier(s):

OSTI ID: 1876845

Grant/Contract Number:  

AC02-05CH11231; F4HBKC4162G001; NNA16BD14C; AC05-00OR22725; SC0012704.

Resource Type:

Published Article

Journal Name:

PRX Quantum

Additional Journal Information:

Journal Name: PRX Quantum Journal Volume: 3 Journal Issue: 2; Journal ID: ISSN 2691-3399

Publisher:

American Physical Society

Country of Publication:

United States

Language:

English

Subject:

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; quantum algorithms; quantum computation; quantum simulation