Quantum simulating continuum field theories with large-spin lattice models

• URL: http://arxiv.org/abs/2412.15325v1
• Date: Thu, 19 Dec 2024 19:00:01 GMT
• Title: Quantum simulating continuum field theories with large-spin lattice models
• Authors: Gabriele Calliari, Marco Di Liberto, Hannes Pichler, Torsten V. Zache,
• Abstract summary: We show how to perform a regularization of scalar QFTs using multi-level or qudit systems. We numerically demonstrate the sequence of extrapolations that leads to quantitative agreement of observables for the integrable sine-Gordon (sG) QFT. Our methods are directly applicable in state-of-the-art analog quantum simulators.
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• 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 using multi-level or qudit systems, and show that this enables quantitative predictions in the continuum limit by extrapolating results obtained for large-spin lattice 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 analyze their scattering dynamics, in agreement with a semi-classical model and analytical predictions. Finally, we illustrate how a non-integrable 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 implementing a wide variety of scalar field theories and tackling long-standing questions in non-equilibrium QFT like the fate of the false vacuum.

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