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Quantum Simulating Continuum Field Theories with Large-Spin Lattice Models

Gabriele Calliari1,2,*, Marco Di Liberto3,4, Hannes Pichler1,2, and Torsten V. Zache1,2,†

  • *Contact author: Gabriele.Calliari@uibk.ac.at
  • †Contact author: Torsten.Zache@uibk.ac.at
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PRX Quantum 6, 030304 – Published 9 July, 2025

DOI: https://doi.org/10.1103/nt76-ttmj

Abstract

Simulating the real-time dynamics of quantum field theories (QFTs) is one of the most promising applications of quantum simulators. Regularizing a bosonic QFT for quantum simulation purposes typically involves a truncation in Hilbert space in addition to a discretization of space. Here, we discuss how to perform such a regularization of scalar QFTs by explicitly constructing suitable many-body lattice Hamiltonians using multilevel or qudit systems and show that this enables quantitative predictions in the continuum limit by extrapolating results obtained for large-spin models. With extensive matrix-product-state simulations, we numerically demonstrate the sequence of extrapolations that leads to quantitative agreement of observables for the integrable sine-Gordon (sG) QFT. We further show how to prepare static and moving-soliton excitations and we analyze their scattering dynamics in the continuum limit, in agreement with a semiclassical model and with quantitative analytical predictions. Finally, we illustrate how a nonintegrable perturbation of the sG model gives rise to dynamics reminiscent of string breaking and plasma oscillations in gauge theories. Our methods are directly applicable in state-of-the-art analog quantum simulators, opening the door to quantitatively investigating a wide variety of scalar-field theories and tackling long-standing questions in nonequilibrium QFT such as the fate of the false vacuum.

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Popular Summary

Quantum field theories (QFTs) play an important role throughout physics, ranging from fundamental descriptions of nature in high-energy physics to the understanding of emergent phenomena in condensed-matter physics. Despite the success of QFTs, our understanding of relevant out-of-equilibrium scenarios such as the real-time dynamics of scattering or the so-called fate of the false vacuum remains incomplete. In this context, quantum simulators promise unique insights—by quantum simulating nonequilibrium QFTs in regimes that are classically inaccessible.

In this work, we provide a precise scheme of how to reach the continuum limit of scalar QFTs on quantum simulators. While QFTs in classical simulations are often regularized on a discrete space-time lattice, quantum simulations of bosonic QFTs require an additional truncation in Hilbert space. Here, we explicitly show that large-spin quantum lattice models provide such a truncation that can be lifted in a controlled way to quantitatively simulate the continuum limit of generic scalar-field theories. We demonstrate the feasibility of our approach with extensive numerical benchmark simulations for a paradigmatic example, the sine-Gordon QFT, both in equilibrium and for the dynamics and scattering of solitonic excitations.

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PRX Quantum 6, 030304– Published 9 July, 2025
  • Received 10 January 2025
  • Revised 9 May 2025
  • Accepted 10 June 2025
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