Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\mathbb{Z}_2$ lattice gauge theories and Kitaev's toric code: A scheme
  for analog quantum simulation   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. 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 of the
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.

2
The categories of this paper are: math
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs