Many-Body Time Evolution from a Correlation-Efficient Quantum Algorithm

TL;DR

The paper presents CETE, a quantum algorithm that efficiently simulates many-body dynamics by correlating only once per time step, reducing circuit depth and enabling longer simulations on near-term quantum devices.

Contribution

CETE introduces a novel correlation-efficient approach that simplifies quantum time evolution by recasting it as a static correlation problem, reducing circuit complexity.

Findings

Successfully simulates hydrogen molecule dynamics

Reduces circuit depth compared to traditional methods

Extends feasible simulation times on near-term devices

Abstract

We introduce the correlation-efficient time-evolution (CETE) algorithm for simulating quantum many-body dynamics. CETE recasts each step of time evolution as a time-independent correlation problem: the ansatz begins from a mean-field single Slater determinant and is then correlated to capture the true time-evolved state. We derive this exact ansatz from a contraction of the time-dependent Schr\"odinger equation onto the space of two electrons. Unlike conventional evolution by sequential short-time propagators, which must both correlate and decorrelate the state as the degree of correlation fluctuates in time, CETE correlates only once. This substantially reduces circuit depth, extending accessible simulation times on near-term quantum devices. We demonstrate the approach by simulating the time evolution of the hydrogen molecule's electronic wavefunction, highlighting the potential for the CETE algorithm to simulate strongly correlated systems on near-term devices.