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

Tomoya Hayata1,2,3,*, Yoshimasa Hidaka4,2,†, and Yuta Kikuchi5,2,‡

  • 1Department of Physics, Keio University School of Medicine, 4-1-1 Hiyoshi, Kanagawa 223-8521, Japan
  • 2RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN, Wako 351-0198, Japan
  • 3International Center for Elementary Particle Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
  • 4Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
  • 5Quantinuum K.K., Otemachi Financial City Grand Cube 3F, 1-9-2 Otemachi, Chiyoda-ku, Tokyo, Japan

  • *Contact author: hayata@keio.jp
  • †Contact author: yoshimasa.hidaka@yukawa.kyoto-u.ac.jp
  • ‡Contact author: yuta.kikuchi@quantinuum.com
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Phys. Rev. Research 8, 033137 – Published 4 August, 2026

DOI: https://doi.org/10.1103/vlpv-n8dy

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 non-Abelian gauge theories in higher dimensions, addressing realistic problems in high-energy physics. To fill the gap, we demonstrate a quantum simulation of real-time dynamics in a (2+1)-dimensional q-deformed 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 SU(2)3, we obtain a simplified yet nontrivial model described by Fibonacci anyons, which preserves the essential non-Abelian fusion structure of the gauge fields. As a demonstration, we 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.

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Phys. Rev. Research 8, 033137– Published 4 August, 2026
  • Received 19 February 2026
  • Accepted 9 July 2026
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