Quantum Algorithm for Simulating Hamiltonian Dynamics with an Off-diagonal Series Expansion

TL;DR

This paper introduces a quantum algorithm that efficiently simulates Hamiltonian dynamics by expanding the time-evolution operator into off-diagonal series, reducing resource requirements compared to existing methods.

Contribution

It presents a novel off-diagonal series expansion approach for quantum simulation that decouples diagonal and off-diagonal dynamics, improving efficiency and resource usage.

Findings

Requires fewer quantum resources than current methods

Optimal dependence on simulation precision

Effective for various Hamiltonian models

Abstract

We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the dynamics due to the diagonal component of the Hamiltonian from the dynamics generated by its off-diagonal part, which we encode using the linear combination of unitaries technique. Our method has an optimal dependence on the desired precision and, as we illustrate, generally requires considerably fewer resources than the current state-of-the-art. We provide an analysis of resource costs for several sample models.