Simulation of adiabatic quantum computing for molecular ground states

TL;DR

This paper introduces a novel classical simulation method for adiabatic quantum state preparation in molecular systems, demonstrating potential speedups and analyzing factors affecting the efficiency of quantum ASP.

Contribution

It presents an adaptive sampling CI approach for simulating ASP with high accuracy and modest resources, and explores strategies to accelerate ASP on quantum hardware.

Findings

Classical simulation of ASP is feasible with negligible error using ASCI.

Starting with a CASCI wavefunction can significantly speed up ASP.

Non-linear interpolation between Hamiltonians does not improve ASP speed.

Abstract

Quantum computation promises to provide substantial speedups in many practical applications with a particularly exciting one being the simulation of quantum many-body systems. Adiabatic state preparation (ASP) is one way that quantum computers could recreate and simulate the ground state of a physical system. In this paper we explore a novel approach for classically simulating the time dynamics of ASP with high accuracy, and with only modest computational resources via an adaptive sampling configuration interaction (ASCI) scheme for truncating the Hilbert space to only the most important determinants. We verify that this truncation introduces negligible error, and use this new approach to simulate ASP for sets of small molecular systems and Hubbard models. Further, we examine two approaches to speeding up ASP when performed on quantum hardware: (i) using the complete active space configuration interaction (CASCI) wavefunction instead of the Hartree-Fock initial state and (ii)~a non-linear interpolation between initial and target Hamiltonians. We find that starting with a CASCI wavefunction with a limited active space yields substantial speedups for many of the systems examined while non-linear interpolation does not. Additionally, we observe interesting trends in the minimum gap location (based on the initial state) as well as how critical time can depend on certain molecular properties such as the number of valence electrons. Importantly, we find that the required state preparation times do not show an immediate exponential wall that would preclude an efficient run of ASP on actual hardware.