Achieving the continuum limit of quantum link lattice gauge theories on quantum devices

Abstract

The solution of gauge theories is one of the most promising applications of quantum technologies. Here, we discuss the approach to the continuum limit for U (1) gauge theories regularized via finite-dimensional Hilbert spaces of quantum spin-S operators, known as quantum link models. For quantum electrodynamics (QED) in one spatial dimension, we numerically demonstrate the continuum limit by extrapolating the ground state energy, the scalar, and the vector meson masses to large spin lengths S, large volume N , and vanishing lattice spacing a. By analytically solving Gauss' law for arbitrary S, we obtain a generalized PXP spin model and count the physical Hilbert space dimension analytically. This allows us to quantify the required resources for reliable extrapolations to the continuum limit on quantum devices. We use a functional integral approach to relate the model with large values of half-integer spins to the physics at topological angle Θ = π. Our findings indicate that quantum devices will in the foreseeable future be able to quantitatively probe the QED regime with quantum link models.

Breaking of the gauge symmetry in lattice gauge theories

“…It would also be important to rephrase and extend the present results to quantum Hamiltonian systems (see Refs. [46,47] for recent works addressing similar issues).…”

Exploring Bosonic and Fermionic Link Models on $(3+1)-$d tubes

“…Note that viewed this way, one way of approaching the Wilson limit of the gauge theory is to consider larger-spin representations [21,22]. It is possible to give a pictorial representation of the QLM, which we show for the case of spin S = 1 2 .…”

Achieving the quantum field theory limit in far-from-equilibrium quantum link models

“…In this work, we have extended to the far-fromequilibrium regime our equilibrium study [75] of the approach of quantum link model regularizations of lattice gauge theories to their quantum field theory limit. We have found that in the thermodynamic limit, the Wilson-Kogut-Susskind limit is achieved over all considered parameter regimes and superselection sectors at already relatively small values of the link spin length S 4, regardless of whether S is half-integer or integer.…”

“…This approximation is very well-suited for current QSM experiments, which are limited in terms of both total Hilbert space and volume. Even though there has recently been works showing that QLM regularizations of lattice gauge theories achieve the quantum field theory limit at relatively small link spin length and system size in equilibrium [74,75], exactly how much QLMs need to scale in the local Hilbert space of the gauge link (parametrized by the link spin length S), the lattice spacing a, and volume in order to achieve this limit in the farfrom-equilibrium regime has remained an open question. Given the recent advancement in large-scale QSM implementations of U(1) quantum link models [26] including experiments on their quench dynamics [27], it is crucial to investigate this question in order to understand how faithfully such experiments can model true high-energy physics phenomena.…”