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

Jinghong Yang1,2,*, Christopher F. Kane1,3,4,†, and Shabnam Jabeen1,2,‡

  • *Contact author: yangjh@umd.edu
  • †Contact author: cfkane24@umd.edu
  • ‡Contact author: jabeen@umd.edu
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Phys. Rev. D 114, 034517 – Published 25 August, 2026

DOI: https://doi.org/10.1103/9yly-8dy7

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 et al. [Science 336, 1130 (2012)] 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.

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Phys. Rev. D 114, 034517– Published 25 August, 2026
  • Received 17 May 2026
  • Accepted 10 July 2026
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