Classical Algorithm for the Mean Value problem over Short-Time Hamiltonian Evolutions

TL;DR

This paper introduces an efficient classical algorithm for approximating the mean value of observables in short-time quantum Hamiltonian evolutions, leveraging Lieb-Robinson bounds to enable scalable simulation of quantum systems.

Contribution

It presents a novel classical simulation method for short-time quantum dynamics that divides large systems into manageable parts using lightcone bounds.

Findings

Algorithm efficiently computes mean values for short-time evolutions.

Uses Lieb-Robinson bounds to limit operator evolution.

Enables classical simulation of certain quantum systems.

Abstract

Simulating physical systems has been an important application of classical and quantum computers. In this article we present an efficient classical algorithm for simulating time-dependent quantum mechanical Hamiltonians over constant periods of time. The algorithm presented here computes the mean value of an observable over the output state of such short-time Hamiltonian evolutions. In proving the performance of this algorithm we use Lieb-Robinson type bounds to limit the evolution of local operators within a lightcone. This allows us to divide the task of simulating a large quantum system into smaller systems that can be handled on normal classical computers.