Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A graph-based formalism for surface codes and twists   Twist defects in surface codes can be used to encode more logical qubits,
improve the code rate, and implement logical gates. In this work we provide a
rigorous formalism for constructing surface codes with twists generalizing the
well-defined homological formalism introduced by Kitaev for describing CSS
surface codes. In particular, we associate a surface code to \emph{any} graph
$G$ embedded on \emph{any} 2D-manifold, in such a way that (1) qubits are
associated to the vertices of the graph, (2) stabilizers are associated to
faces, (3) twist defects are associated to odd-degree vertices. In this way, we
are able to reproduce the variety of surface codes, with and without twists, in
the literature and produce some new examples. We also calculate and bound
various code properties such as the rate and distance in terms of topological
graph properties such as genus, systole, and face-width.

11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio