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arXiv:2009.07848

Fate of Lattice Gauge Theories Under Decoherence

Jad C. Halimeh, Valentin Kasper, Philipp Hauke

Published Sep 16, 2020• 12 citations
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Abstract

A major test of the capabilities of modern quantum simulators and NISQ devices is the reliable realization of gauge theories, which constitute a gold standard of implementational efficacy. In addition to unavoidable unitary errors, realistic experiments suffer from decoherence, which compromises gauge invariance and, therefore, the gauge theory itself. Here, we study the effect of decoherence on the quench dynamics of a lattice gauge theory. Rigorously identifying the gauge violation as a divergence measure in the gauge sectors, we find at short times that it first grows diffusively $\simγt$ due to decoherence at environment-coupling strength $γ$, before unitary errors at strength $λ$ dominate and the violation grows ballistically $\simλ^2t^2$. We further introduce multiple quantum coherences in the context of gauge theories to quantify decoherence effects. Both experimentally accessible measures will be of independent interest beyond the immediate context of this work.

DOI
10.48550/arxiv.2009.07848

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A major test of the capabilities of modern quantum simulators and NISQ devices is the reliable realization of gauge theories, which constitute a gold standard of implementational efficacy. In addition to unavoidable unitary errors, realistic experiments suffer from decoherence, which compromises gauge invariance and, therefore, the gauge theory itself. Here, we study the effect of decoherence on the quench dynamics of a lattice gauge theory. Rigorously identifying the gauge violation as a divergence measure in the gauge sectors, we find at short times that it first grows diffusively ∼γt\simγt∼γt due to decoherence at environment-coupling strength γγγ, before unitary errors at strength λλλ dominate and the violation grows ballistically ∼λ2t2\simλ^2t^2∼λ2t2. We further introduce multiple quantum coherences in the context of gauge theories to quantify decoherence effects. Both experimentally accessible measures will be of independent interest beyond the immediate context of this work.
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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.
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Suppression of 1/f1/f1/f noise in quantum simulators of gauge theories
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The dynamics of lattice gauge theories is characterized by an abundance of local symmetry constraints. Although errors that break gauge symmetry appear naturally in NISQ-era quantum simulators, their influence on the gauge-theory dynamics is insufficiently investigated. As we show, a small gauge breaking of strength λλλ induces a staircase of long-lived prethermal plateaus. The number of prethermal plateaus increases with the number of matter fields LLL, with the last plateau being reached at a timescale λ−L/2λ^{-L/2}λ−L/2, showing an intimate relation of the concomitant slowing down of dynamics with the number of local gauge constraints. Our results bode well for NISQ quantum devices, as they indicate that the proliferation timescale of gauge-invariance violation is counterintuitively delayed exponentially in system size.