Iteration-free digital quantum simulation of imaginary-time evolution based on the approximate unitary expansion

¹ China Mobile (Suzhou) Software Technology Company Limited - Suzhou 215163, China
² Department of Physics, College of Science, North China University of Technology - Beijing 100144, China

^(a) E-mail: wjw17@tsinghua.org.cn (corresponding author)
^(b) E-mail: czheng@ncut.edu.cn (corresponding author)

Received: 21 December 2022
Accepted: 1 March 2023

Abstract

Imaginary-time evolution plays an important role in many areas of quantum physics and has been widely applied to the ground-state determination of various Hamiltonian in the quantum computation field. In this work, we propose an iteration-free quantum algorithm in a full gate-based frame using the approximate unitary expansion to simulate the imaginary-time evolution operator, avoiding the resource overhead caused by repeated measurement for state reconstruction or complex pre-calculations in the classical computers. We detail the algorithm and analyze the complexity and related characteristics including a lower bound for ancillary qubits at a given success probability. Then an application demonstration of the algorithm in quantum chemistry with hydrogen molecule under noiseless and noisy conditions is offered. In addition, we present another imaginary-time evolution simulation method based on similar construction schemes. Our algorithms can serve as the alternative proposals for the imaginary-time evolution realization in the future fault-tolerant quantum computers.