Fate of Lattice Gauge Theories Under Decoherence

Understand

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 $\sim\gamma t$ due to decoherence at environment-coupling strength $\gamma$, before unitary errors at strength $\lambda$ dominate and the violation grows ballistically $\sim\lambda^2t^2$.