Computing Ground State Properties with Early Fault-Tolerant Quantum Computers

TL;DR

This paper introduces a hybrid quantum-classical algorithm designed to efficiently estimate ground state properties of molecules and materials using low-depth circuits on early fault-tolerant quantum computers, enabling industry-relevant calculations.

Contribution

It presents a novel hybrid algorithm for estimating ground state properties beyond energy, suitable for early fault-tolerant quantum devices, with detailed cost analysis.

Findings

Efficient estimation of Green's functions and density matrices with low-depth circuits.

Analysis of costs as a function of accuracy, spectral gap, and initial overlap.

Provides a practical approach for industry-relevant quantum molecular calculations.

Abstract

Significant effort in applied quantum computing has been devoted to the problem of ground state energy estimation for molecules and materials. Yet, for many applications of practical value, additional properties of the ground state must be estimated. These include Green's functions used to compute electron transport in materials and the one-particle reduced density matrices used to compute electric dipoles of molecules. In this paper, we propose a quantum-classical hybrid algorithm to efficiently estimate such ground state properties with high accuracy using low-depth quantum circuits. We provide an analysis of various costs (circuit repetitions, maximal evolution time, and expected total runtime) as a function of target accuracy, spectral gap, and initial ground state overlap. This algorithm suggests a concrete approach to using early fault tolerant quantum computers for carrying out industry-relevant molecular and materials calculations.