Estimating truncation effects of quantum bosonic systems using sampling algorithms

TL;DR

This paper presents a classical sampling approach using Markov Chain Monte Carlo to estimate truncation errors in simulating bosonic systems on quantum computers, enabling better resource planning and validation of quantum simulations.

Contribution

It introduces a classical sampling method to estimate truncation effects in bosonic quantum simulations, applicable to large systems beyond exact diagonalization capabilities.

Findings

Successfully applied to 2D scalar field theory on large lattices

Provides a practical way to estimate quantum resource requirements

Enables validation of quantum simulation results

Abstract

To simulate bosons on a qubit- or qudit-based quantum computer, one has to regularize the theory by truncating infinite-dimensional local Hilbert spaces to finite dimensions. In the search for practical quantum applications, it is important to know how big the truncation errors can be. In general, it is not easy to estimate errors unless we have a good quantum computer. In this paper, we show that traditional sampling methods on classical devices, specifically Markov Chain Monte Carlo, can address this issue for a rather generic class of bosonic systems with a reasonable amount of computational resources available today. As a demonstration, we apply this idea to the scalar field theory on a two-dimensional lattice, with a size that goes beyond what is achievable using exact diagonalization methods. This method can be used to estimate the resources needed for realistic quantum simulations of bosonic theories, and also, to check the validity of the results of the corresponding quantum simulations.