Z2 Lattice Gauge Theories and Kitaev’s Toric Code: A Scheme for Analog Quantum Simulation

Kitaev’s toric code is an exactly solvable model with Z2-topological order, which has potential applications in quantum computation and error correction. Direct experimental realization re-mains an open challenge. Here we propose a building block for Z2 lattice gauge theories coupled to dynamical matter and demonstrate how it allows for an implementation of the toric-code groundstate and its topological excitations. The proposed building block is realized in the second-order coupling regime and is well-suited for implementations with superconducting qubits. Furthermore, we propose a pathway to prepare topologically non-trivial initial states during which a large gap on the order of the underlying coupling strength is present.This is verified by both analytical arguments and numerical studies. Moreover, we outline experimental signatures of the ground-state wavefunction and introduce a minimal braiding protocol. Detecting a \pi-phase shift between Ramsey fringes in this protocol reveals the anyonic excitations ofthe toric-code Hamiltonian in a system with only three triangular plaquettes. Our work paves the way for realizing non-Abelian anyons in analog quantum simulators.

[publication in progress]