$\mathbb{Z}_2$ lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation

Understand

Kitaev's toric code is an exactly solvable model with $\mathbb{Z}_2$-topological order, which has potential applications in quantum computation and error correction.

• However, a direct experimental realization remains an open challenge.
• Here, we propose a building block for $\mathbb{Z}_2$ lattice gauge theories coupled to dynamical matter and demonstrate how it allows for an implementation of the toric-code ground state and its topological excitations.
• This is achieved by introducing separate matter excitations on individual plaquettes, whose motion induce the required plaquette terms.