Generating Approximate Ground States of Strongly Correlated Quantum Many-Body Systems Through Quantum Imaginary Time Evolution

TL;DR

This paper explores the effectiveness of Quantum Imaginary Time Evolution (QITE) in approximating ground states of complex quantum systems, demonstrating its potential for early fault-tolerant quantum computers and comparing it with classical methods.

Contribution

It provides a heuristic analysis of QITE's ability to approximate ITE for lattice and molecular Hamiltonians, including the use of fermionic Gaussian states as initial states.

Findings

QITE can qualitatively replicate ITE behavior in various systems.

QITE improves over classical mean-field solutions in tested cases.

Fermionic Gaussian states serve as efficient initial states for quantum simulations.

Abstract

Most quantum algorithms designed to generate or probe properties of the ground state of a quantum many-body system require as input an initial state with a large overlap with the desired ground state. One approach for preparing such a ground state is Imaginary Time Evolution (ITE). Recent work by [Motta, M., Sun, C., Tan, A.T.K. et al. (2020)] introduced an algorithm -- which we will refer to as Quantum Imaginary Time Evolution (QITE) -- that shows how ITE can be approximated by a sequence of unitary operators, making QITE potentially implementable on early fault-tolerant quantum computers. In this work, we provide a heuristic study of the capabilities of the QITE algorithm in approximating the ITE of lattice and molecular electronic structure Hamiltonians. We numerically study the performance of the QITE algorithm when provided with a good classical initial state for a large class of systems, some of which are of interest to industrial applications, and check if QITE is able to qualitatively replicate the ITE behavior and improve over a classical mean-field solution. The systems we consider in this work range from one- and two-dimensional lattice systems of various lattice geometries displaying short- and long-range interactions, to active spaces of molecular electronic structure Hamiltonians. In addition to the comparison of QITE and ITE, we explicitly show how imaginary time evolved fermionic Gaussian states can serve as initial states which can be efficiently computed on classical computers and efficiently implemented on quantum computers for generic spin Hamiltonians in arbitrary lattice geometries and dimensions, which can be of independent interest.