Constructing U(1) gauge symmetry in electronic circuits


Classical electronic circuits have proven powerful to study topological lattice structures. At the same time quantum simulators reach for increasingly complex lattice gauge theories with the goal of simulating processes in high energy physics. This work aims to connect these two fields by building a classical electronic circuit that approximates a U(1) gauge symmetric Hamiltonian. The circuit is constructed as an extention of the one-dimensional, topological Su-Schrieffer-Heeger model and we measure the time evolution in small system realizations with lattice sizes of up to three sites. The measurements qualitatively match theoretical expectations and agree with quantitative predictions where available. We develop a measure for the violation of local conserved quantities associated with gauge symmetry as benchmark for simulator quality. Since electronic circuits are fast in prototyping and of low cost, this platform provides a pathway to the classical regimes of non-abelian theories possibly faster than quantum simulators.