Entanglement accelerates quantum simulation

TL;DR

This paper explores how quantum entanglement influences simulation efficiency, demonstrating that entanglement can both hinder classical methods and enhance quantum algorithms through new bounds and adaptive techniques.

Contribution

It introduces a tighter error bound related to entanglement entropy and an adaptive simulation algorithm that leverages measurement gadgets.

Findings

Product-formula approximations perform better for entangled systems.

Tighter upper bounds for simulation error based on entanglement entropy.

Entanglement can be exploited to accelerate quantum algorithms.

Abstract

Quantum entanglement is an essential feature of many-body systems that impacts both quantum information processing and fundamental physics. The growth of entanglement is a major challenge for classical simulation methods. In this work, we investigate the relationship between quantum entanglement and quantum simulation, showing that product-formula approximations can perform better for entangled systems. We establish a tighter upper bound for algorithmic error in terms of entanglement entropy and develop an adaptive simulation algorithm incorporating measurement gadgets to estimate the algorithmic error. This shows that entanglement is not only an obstacle to classical simulation, but also a feature that can accelerate quantum algorithms.