A resource-efficient quantum-classical hybrid algorithm for energy gap evaluation

TL;DR

This paper introduces a resource-efficient hybrid quantum-classical algorithm that estimates energy gaps in quantum many-body systems without requiring controlled evolution, avoiding barren plateaus, and verified through classical simulations.

Contribution

It presents a non-variational hybrid algorithm using Monte Carlo and real-time simulation, simplifying implementation and addressing barren plateau issues.

Findings

Successful numerical simulations on Heisenberg model

Effective energy gap estimation without controlled evolution

Algorithm avoids barren plateaus

Abstract

Estimating the eigenvalue or energy gap of a Hamiltonian H is vital for studying quantum many-body systems. Particularly, many of the problems in quantum chemistry, condensed matter physics, and nuclear physics investigate the energy gap between two eigenstates. Hence, how to efficiently solve the energy gap becomes an important motive for researching new quantum algorithms. In this work, we propose a hybrid non-variational quantum algorithm that uses the Monte Carlo method and real-time Hamiltonian simulation to evaluate the energy gap of a general quantum many-body system. Compared to conventional approaches, our algorithm does not require controlled real-time evolution, thus making its implementation much more experimental-friendly. Since our algorithm is non-variational, it is also free from the "barren plateaus" problem. To verify the efficiency of our algorithm, we conduct numerical simulations for the Heisenberg model and molecule systems on a classical emulator.