Topological Subsystem Codes From Graphs and Hypergraphs

Understand

Topological subsystem codes were proposed by Bombin based on 3-face-colorable cubic graphs.

• Suchara, Bravyi and Terhal generalized this construction and proposed a method to construct topological subsystem codes using 3-valent hypergraphs that satisfy certain constraints.
• Finding such hypergraphs and computing their parameters however is a nontrivial task.
• We propose families of topological subsystem codes that were previously not known.