Quantum-simulator hardware promises new insights into problems from particle and nuclear physics. A major challenge is to reproduce gauge invariance, as violations of this quintessential property of lattice gauge theories can have dramatic consequences, e.g., the generation of a photon mass in quantum electrodynamics. Here, we introduce an experimentally simple method to controllably protect gauge invariance in U(1) lattice gauge theories against coherent errors, employing energy-penalty terms consisting only of single-body terms, which can be implemented with single-qubit gates or local chemical potentials. As we derive analytically, special sets of penalty coefficients render undesired gauge sectors inaccessible by any unitary dynamics for at least exponentially long times. In this way, the gauge-invariant subspace is protected by an emergent global symmetry, meaning the discussed method can also be immediately applied to other symmetries. In our numerical benchmarks for continuous-time and digital quantum simulations, gauge protection holds for all calculated evolution times (up to t>1010/J for continuous time, with J the relevant energy scale). Crucially, our gauge-protection technique is simpler to realize than the associated ideal gauge theory, and can thus be readily implemented in current ultracold-atom analog simulators as well as digital NISQ devices.
J. C. Halimeh, H. Lang, J. Mildenberger, Z. Jiang, and P. Hauke, “Gauge-Symmetry Protection
Using Single-Body Terms”, arXiv:2007.00668 (2020).
Related to Project B04