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

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.

24 pages, 8 figures

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