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

Tomoya Hayata, Yoshimasa Hidaka, Yuta Kikuchi

TL;DR

The work tackles real-time dynamics of nonabelian lattice gauge theories, which are difficult to access with classical simulations due to the sign problem. It realizes a simplified (2+1)-D $q$-deformed $SU(2)_3$ model on a honeycomb lattice using Fibonacci anyons, with dynamics encoded through explicit $F$-moves that implement the nonabelian fusion rule $\tau\times\tau=1+\tau$ and a Hamiltonian $H_{YM}=H_E+H_M$. An 18-qubit trapped-ion experiment demonstrates a second-order Trotter evolution with up to 47 $F$-moves per step, identifies memory noise on idle qubits as the dominant error source, and mitigates it via dynamical decoupling and parallelized circuit design complemented by a variational CPflow compression. The results validate the feasibility of nonabelian gauge-theory simulations on noisy quantum hardware and point toward scaling to richer theories such as $SU(2)_k$ or $SU(3)_k$ with possible matter fields.

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.

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

TL;DR

The work tackles real-time dynamics of nonabelian lattice gauge theories, which are difficult to access with classical simulations due to the sign problem. It realizes a simplified (2+1)-D -deformed model on a honeycomb lattice using Fibonacci anyons, with dynamics encoded through explicit -moves that implement the nonabelian fusion rule and a Hamiltonian . An 18-qubit trapped-ion experiment demonstrates a second-order Trotter evolution with up to 47 -moves per step, identifies memory noise on idle qubits as the dominant error source, and mitigates it via dynamical decoupling and parallelized circuit design complemented by a variational CPflow compression. The results validate the feasibility of nonabelian gauge-theory simulations on noisy quantum hardware and point toward scaling to richer theories such as or with possible matter fields.

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 -deformed Yang-Mills theory using a trapped-ion quantum computer. By restricting the irreducible representations of the gauge fields to the integer-spin sector of , 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 -moves. In our demonstrations, the quantum circuits execute up to 47 sequential -moves. We identify idling errors as the dominant error source, which can be effectively mitigated using dynamical decoupling combined with a parallelized implementation of -moves.
Paper Structure (11 sections, 42 equations, 3 figures)

This paper contains 11 sections, 42 equations, 3 figures.

Table of Contents

  1. Introduction
  2. q-deformed Yang-Mills theory on a honeycomb lattice
  3. Methods
  4. Model
  5. Gate decomposition
  6. Experiments
  7. Outlook
  8. Measurement of the Wilson loop operator
  9. Experimental details
  10. Explicit construction of the first Trotter step
  11. Explicit construction of the general Trotter steps

Figures (3)

  • Figure 1: Qubit layout simulated in experiments.
  • Figure 2: Classical noiseless simulation of the $K$ dependence of the thermalization dynamics. The fast thermalization is realized at $K=0.5$ around $t=3.0$.
  • Figure 3: Experimental results of the thermalization dynamics. Blue squares represent the classical noiseless simulations of the quantum circuits used in experiments. Red triangles and green circles represent experimental results without and with dynamical decoupling. The solid curves represent the classical noiseless simulations with a very small Trotter step, shown as the exact numerical simulations.