Probing confinement in a $\mathbb{Z}_2$ lattice gauge theory on a quantum computer

TL;DR

This paper demonstrates quantum simulation of confinement in a $ ext{Z}_2$ lattice gauge theory using a superconducting quantum processor, revealing how gauge constraints influence dynamics and can be modified or protected.

Contribution

It presents the first digital quantum simulation of confinement in a $ ext{Z}_2$ gauge theory on a superconducting quantum computer, exploring gauge constraint effects and modifications.

Findings

Confinement of charges observed through electric field coupling.

Modification from $ ext{Z}_2$ to $ ext{U}(1)$ symmetry freezes system dynamics.

Gauge constraints significantly restrict lattice gauge theory evolution.

Abstract

Gauge theories describe the fundamental forces in the standard model of particle physics and play an important role in condensed matter physics. The constituents of gauge theories, for example charged matter and electric gauge field, are governed by local gauge constraints, which lead to key phenomena such as confinement of particles that are not fully understood. In this context, quantum simulators may address questions that are challenging for classical methods. While engineering gauge constraints is highly demanding, recent advances in quantum computing are beginning to enable digital quantum simulations of gauge theories. Here, we simulate confinement dynamics in a $\mathbb{Z}_2$ lattice gauge theory on a superconducting quantum processor. Tuning a term that couples only to the electric field produces confinement of charges, a manifestation of the tight bond that the gauge constraint generates between both. Moreover, we show how a modification of the gauge constraint from $\mathbb{Z}_2$ towards $\mathrm{U}(1)$ symmetry freezes the system dynamics. Our work illustrates the restriction that the underlying gauge constraint imposes on the dynamics of a lattice gauge theory, it showcases how gauge constraints can be modified and protected, and it promotes the study of other models governed by multi-body interactions.