Tightening energy-based boson truncation bound using Monte Carlo-assisted methods

TL;DR

This paper introduces a new Monte Carlo-assisted method to tighten energy-based boson truncation bounds in quantum field theory simulations, reducing systematic uncertainties related to finite-dimensional Hilbert space representations.

Contribution

It presents an improved analytic derivation combined with a Monte Carlo numerical procedure to significantly tighten boson truncation bounds in quantum simulations.

Findings

Reduces volume dependence of the truncation cutoff

Achieves bounds nearly proportional to volume in some cases

Mitigates systematic uncertainties in quantum field theory simulations

Abstract

Quantum simulation offers a promising framework for quantum field theory calculations. Obtaining reliable results, however, requires careful characterization of systematic uncertainties. One important source is the boson truncation error, which arises from representing infinite-dimensional local Hilbert spaces with finite-dimensional ones. Previous studies have examined this problem from several perspectives. In particular, Jordan, Lee, and Preskill (arXiv:1111.3633) derived an energy-based bound applicable to generic low-energy states across a broad class of field theories. However, this approach often yields overly conservative bounds, especially at large volumes. In this work, we introduce a new methodology that significantly tightens the energy-based boson truncation bound through two complementary advances: an improved analytic derivation and a Monte Carlo-based numerical procedure. We demonstrate the method in (1+1)-dimensional scalar field theory and (2+1)-dimensional U(1) gauge theory in the dual formalism. Our approach substantially mitigates the volume dependence of the required truncation cutoff, achieving reductions nearly proportional to the volume in some cases and to the square root of the volume in others.