Gauge-Symmetry Protection Using Single-Body Terms

• URL: http://arxiv.org/abs/2007.00668v2
• Date: Tue, 11 Aug 2020 15:36:45 GMT
• Title: Gauge-Symmetry Protection Using Single-Body Terms
• Authors: Jad C. Halimeh, Haifeng Lang, Julius Mildenberger, Zhang Jiang, Philipp Hauke
• Abstract summary: Quantum-simulator hardware promises new insights into problems from particle and nuclear physics. We introduce an experimentally friendly method to protect gauge invariance in lattice gauge theories. Our method employs only single-body energy-penalty terms, thus enabling practical implementations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 friendly method to protect gauge invariance in $\mathrm{U}(1)$ lattice gauge theories against coherent errors in a controllable way. Our method employs only single-body energy-penalty terms, thus enabling practical implementations. As we derive analytically, some sets of penalty coefficients render undesired gauge sectors inaccessible by unitary dynamics for exponentially long times, and, for few-body error terms, with resources independent of system size. These findings constitute an exponential improvement over previously known results from energy-gap protection or perturbative treatments. In our method, the gauge-invariant subspace is protected by an emergent global symmetry, meaning it can 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 $t>10^{10}/J$ 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 noisy intermediate scale quantum (NISQ) devices.

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