Topological subsystem codes from graphs and hypergraphs

Topological subsystem codes from graphs and hypergraphs

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 ...

Topological subsystem codes

On codes from hypergraphs

We propose a new family of asymptotically good binary codes, generalizing previous constructions of expander codes to -uniform hypergraphs. We also describe an efficient decoding algorithm for these codes, that for a certain region of rates improves the known results for decoding distance of expander codes. The construction is based on hypergraphs with a certain “expansion” property called here...

Quantum Stabilizer and Subsystem Codes from Algebro-geometric Toric Codes

We show how to construct quantum stabilizer and subsystem codes from algebro-geometric toric codes extending the known construction of subsystem codes from cyclic codes and extending the construction of stabilizer codes from toric codes in an earlier work by one of the authors. Since algebrogeometric toric codes are higher dimensional extensions of cyclic codes, we obtain this way a new and ric...

Subsystem Codes

We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem codes using a counting argument similar to the quantum Gilbert-Varshamov bound. We derive linear programming bounds and other upper bounds. We answer the qu...