Onset of thermalization of q-deformed SU(2) Yang-Mills theory on a trapped-ion quantum computer

TL;DR

This paper demonstrates the first quantum simulation of thermalization in a (2+1)-dimensional q-deformed SU(2) Yang-Mills theory using a trapped-ion quantum computer, advancing high-energy physics applications in quantum computing.

Contribution

It introduces a quantum simulation of a nonabelian gauge theory in higher dimensions, specifically a q-deformed SU(2) Yang-Mills model, using trapped ions and explicit F-move circuits.

Findings

Successfully simulated real-time dynamics with up to 47 F-moves.

Identified idling errors as dominant and mitigated them with dynamical decoupling.

Showed feasibility of simulating nonabelian gauge theories on quantum hardware.

Abstract

Nonequilibrium dynamics of quantum many-body systems is one of the main targets of quantum simulations. This focus - together with rapid advances in quantum-computing hardware - has driven increasing applications in high-energy physics, particularly in lattice gauge theories. However, most existing experimental demonstrations remain restricted to (1+1)-dimensional and/or abelian gauge theories, such as the Schwinger model and the toric code. It is essential to develop quantum simulations of nonabelian gauge theories in higher dimensions, addressing realistic problems in high-energy physics. To fill the gap, we demonstrate a quantum simulation of thermalization dynamics in a (2+1)-dimensional $q$-deformed $\mathrm{SU}(2)_3$ Yang-Mills theory using a trapped-ion quantum computer. By restricting the irreducible representations of the gauge fields to the integer-spin sector of $\mathrm{SU}(2)_3$, we obtain a simplified yet nontrivial model described by Fibonacci anyons, which preserves the essential nonabelian fusion structure of the gauge fields. We successfully simulate the real-time dynamics of this model using quantum circuits that explicitly implement $F$-moves. In our demonstrations, the quantum circuits execute up to 47 sequential $F$-moves. We identify idling errors as the dominant error source, which can be effectively mitigated using dynamical decoupling combined with a parallelized implementation of $F$-moves.