Symmetry verification for noisy quantum simulations of non-Abelian lattice gauge theories

Edoardo Ballini; Julius Mildenberger; Matteo M. Wauters; Philipp Hauke

doi:10.22331/q-2025-07-22-1802

Symmetry verification for noisy quantum simulations of non-Abelian lattice gauge theories

Edoardo Ballini, Julius Mildenberger, Matteo M. Wauters, and Philipp Hauke

Pitaevskii BEC Center and Department of Physics, University of Trento, Via Sommarive 14, I-38123 Trento, Italy
INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy

Published:	2025-07-22, volume 9, page 1802
Editor:	Mohan Sarovar
Eprint:	arXiv:2412.07844v3
Doi:	https://doi.org/10.22331/q-2025-07-22-1802
Citation:	Quantum 9, 1802 (2025).

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Abstract

Non-Abelian gauge theories underlie our understanding of fundamental forces of modern physics. Simulating them on quantum hardware is an outstanding challenge in the rapidly evolving field of quantum simulation. A key prerequisite is the protection of local gauge symmetries against errors that, if unchecked, would lead to unphysical results. While an extensive toolkit devoted to identifying, mitigating, and ultimately correcting such errors has been developed for Abelian groups, non-commuting symmetry operators complicate the implementation of similar schemes in non-Abelian theories. Here, we discuss two techniques for error mitigation through symmetry verification, tailored for non-Abelian lattice gauge theories implemented in noisy qudit hardware: dynamical post-selection (DPS), based on mid-circuit measurements without active feedback, and post-processed symmetry verification (PSV), which combines measurements of correlations between target observables and gauge transformations. We illustrate both approaches for the discrete non-Abelian group $D_3$ in 2+1 dimensions, explaining their usefulness for current NISQ devices even in the presence of fast fluctuating noise. Our results open new avenues for robust quantum simulation of non-Abelian gauge theories, for further development of error-mitigation techniques, and for measurement-based control methods in qudit platforms.

Featured image: (a) Errors in the quantum simulation of an LGT model couple the physical (gauge-invariant) sector $\mathcal{H}_P$ with the rest of the Hilbert space $\mathcal{H}_Q$. We model errors by a generic noise channel $\mathcal{E}$ added to the desired evolution operator $\mathcal{U}_{\Delta t}$. (b) Illustration of the two schemes, DPS (solid line) and PSV (dot-dashed). Both techniques dramatically improve the recovered system dynamics over the simple average over trajectories subject to $\mathcal{E}$ (dashed). DPS is able to follow the exact Trotterized dynamics (bullets) for longer times. Ensemble-averages over 5000 trajectories with coupling $1/g^2=0.5$, Trotter step $\Delta t/a =0.25$, and noise strength $\gamma=0.2$. (c-d) Simplified circuit schematics. (c) DPS is based on mid-circuit validations of the Gauss' laws (potentially delaying the measurements and without requiring active feedback). (d) PSV post-processes data acquired from different measurement settings in order to reconstruct gauge-invariant observables.

Popular summary

Quantum hardware can be used to simulate key theories of our description of nature such as lattice gauge theories (LGTs). However, existing quantum devices are error prone, making it crucial to protect gauge symmetries during the simulation. Post-selection is a cheap yet effective tool to extract meaningful physical results from noisy runs. In the important case where the symmetries are non-Abelian, however, the picture becomes significantly more complicated as standard approaches cannot simultaneously verify invariance under noncommuting transformations. In this work, we discuss two extensions of post-selection tailored to the quantum simulations of non-Abelian LGTs in qudit hardware and study their efficacy as error-mitigation strategies. The first, dynamical post-selection (DPS) is based on a quantum Zeno regime arising from repeated weak measurements. The second, post-processed symmetry verification (PSV), leverages the structure of gauge transformations to extract the gauge-invariant contribution of an observable from a collection of correlations. Both methods succeed in recovering reliable dynamics long after physical information has been washed out in the bare noisy dynamics and are well suited for state-of-the-art qudit platforms.

► BibTeX data

@article{Ballini2025symmetry,
  doi = {10.22331/q-2025-07-22-1802},
  url = {https://doi.org/10.22331/q-2025-07-22-1802},
  title = {Symmetry verification for noisy quantum simulations of non-{A}belian lattice gauge theories},
  author = {Ballini, Edoardo and Mildenberger, Julius and Wauters, Matteo M. and Hauke, Philipp},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1802},
  month = jul,
  year = {2025}
}

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