Simulating Hamiltonian dynamics with a truncated Taylor series

TL;DR

This paper presents a simplified and efficient quantum algorithm for simulating Hamiltonian dynamics using a truncated Taylor series, achieving optimal precision dependence and broad applicability.

Contribution

It introduces a streamlined method for Hamiltonian simulation on quantum computers by directly implementing linear combinations of unitaries for the truncated Taylor series.

Findings

Cost depends logarithmically on inverse precision, which is optimal.

Simplifies previous algorithms through direct linear combination implementation.

Applicable to a wide range of physical systems.

Abstract

We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of physical systems. As in another recent algorithm, the cost of our method depends only logarithmically on the inverse of the desired precision, which is optimal. However, we simplify the algorithm and its analysis by using a method for implementing linear combinations of unitary operations to directly apply the truncated Taylor series.