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A major test of the capabilities of modern quantum simulators and NISQdevices is the reliable realization of gauge theories, which constitute a goldstandard of implementational efficacy. In addition to unavoidable unitaryerrors, realistic experiments suffer from decoherence, which compromises gaugeinvariance and, therefore, the gauge theory itself. Here, we study the effectof decoherence on the quench dynamics of a lattice gauge theory. Rigorouslyidentifying the gauge violation as a divergence measure in the gauge sectors,we find at short times that it first grows diffusively $\sim\gamma t$ due todecoherence at environment-coupling strength $\gamma$, before unitary errors atstrength $\lambda$ dominate and the violation grows ballistically$\sim\lambda^2t^2$. We further introduce multiple quantum coherences in thecontext of gauge theories to quantify decoherence effects. Both experimentallyaccessible measures will be of independent interest beyond the immediatecontext of this work.

Fate of Lattice Gauge Theories Under Decoherence