Fuzzy gauge theory for quantum computers

TL;DR

This paper introduces fuzzy gauge theory, a new qubitization approach for continuous gauge theories on quantum computers, which approximates the theories with finite degrees of freedom while maintaining key properties.

Contribution

The paper proposes a novel fuzzy gauge theory method for quantum simulation, extending fuzzy models to gauge theories and demonstrating its universality and resource efficiency.

Findings

Fuzzy gauge theory lies in the same universality class as regular gauge theory.

The models are resource-efficient for quantum simulations.

The approach potentially eliminates the need for additional limits besides the spatial continuum limit.

Abstract

Continuous gauge theories, because of their bosonic degrees of freedom, have an infinite-dimensional local Hilbert space. Encoding these degrees of freedom on qubit-based hardware demands some sort of ``qubitization'' scheme, where one approximates the behavior of a theory while using only finitely many degrees of freedom. We propose a novel qubitization strategy for gauge theories, called ``fuzzy gauge theory,'' building on the success of the fuzzy $\sigma$-model in earlier work. We provide arguments that the fuzzy gauge theory lies in the same universality class as regular gauge theory, in which case its use would obviate the need of any further limit besides the usual spatial continuum limit. Furthermore, we demonstrate that these models are relatively resource-efficient for quantum simulations.