An efficient finite-resource formulation of non-Abelian lattice gauge theories beyond one dimension

TL;DR

This paper introduces a resource-efficient quantum and tensor-network method to compute the running of the coupling in non-Abelian lattice gauge theories beyond one dimension, addressing limitations of classical approaches.

Contribution

It presents a novel Hamiltonian formulation using loop variables and a local basis to enable quantum computations of gauge theories beyond one dimension.

Findings

Allows computations at arbitrary couplings and lattice spacings

Enables simulations with current quantum hardware and tensor networks

Addresses limitations of classical methods in continuum extrapolation

Abstract

Non-Abelian gauge theories provide the most accurate description of fundamental interactions, showing remarkable agreement with experimental data in cosmology and particle physics. Highly precise predictions can be made using standard techniques, both in the continuum and in the lattice frameworks. However, classical methods have limitations, particularly when attempting to extrapolate the continuum limit from the study of lattice gauge theories. Complementing classical computations or combining them with quantum computational methods, to improve the predictions towards the continuum limit with current quantum resources, is a formidable open challenge. In this paper, we propose a resource-efficient method to compute the running of the coupling in non-Abelian gauge theories beyond one spatial dimension. We first represent the Hamiltonian on periodic lattices in terms of loop variables and conjugate loop electric fields, exploiting the Gauss law to retain the gauge-independent ones. Then, we identify a local basis for small and large loops variationally to minimize the truncation error while computing the running of the coupling on small tori. Our method enables computations at arbitrary values of the bare coupling and lattice spacing with current quantum computers, simulators and tensor-network calculations, in regimes otherwise inaccessible.