Homological Stabilizer Codes

Understand

In this paper we define homological stabilizer codes which encompass codes such as Kitaev's toric code and the topological color codes.

• These codes are defined solely by the graphs they reside on.
• This feature allows us to use properties of topological graph theory to determine the graphs which are suitable as homological stabilizer codes.
• We then show that all toric codes are equivalent to homological stabilizer codes on 4-valent graphs.