Abstract
Currently, there are intense experimental efforts to realize lattice gauge theories in quantum simulators. Except for specific models, however, practical quantum simulators can never be fine-tuned to perfect local gauge invariance. There is thus a strong need for a rigorous understanding of gauge-invariance violation and how to reliably protect against it. As we show through analytic and numerical evidence, in the presence of a gauge invariance-breaking term the gauge violation accumulates only perturbatively at short times before proliferating only at very long times. This proliferation can be suppressed up to infinite times by energetically penalizing processes that drive the dynamics away from the initial gauge-invariant sector. Our results provide a theoretical basis that highlights a surprising robustness of gauge-theory quantum simulators.
Highlights
Introduction.—In modern physics, gauge theories assume a central role, ranging from the Standard Model of Particle Physics [1] to emergent exotic solid-state phases [2, 3]
Still in the developmental phase, these experiments are rapidly advancing [10,11,12,13,14,15,16,17,18], making one open issue all the more pressing: how can we ensure the reliability of quantum simulators once they scale beyond problems that can be benchmarked by classical computers [19, 20]? For gauge theories, this issue is subtle, since a faithful quantum simulation necessitates the correct engineering of the Hamiltonian dynamics, but crucially of the defining local gauge symmetry
As we show in this Letter, quantum simulators can reliably reproduce the out-of-equilibrium dynamics of gauge theories even if the prohibitive restriction of perfect gauge invariance is relaxed
Summary
As we show through analytic and numerical evidence, in the presence of a gauge invariance-breaking term the gauge violation accumulates only perturbatively at short times before proliferating only at very long times. This proliferation can be suppressed up to infinite times by energetically penalizing processes that drive the dynamics away from the initial gauge-invariant sector. This issue is subtle, since a faithful quantum simulation necessitates the correct engineering of the Hamiltonian dynamics, but crucially of the defining local gauge symmetry.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
