Topological subsystem codes from graphs and hypergraphs

摘要

Topological subsystem codes were proposed by Bombin based on 3-face-colorable cubic graphs. Suchara,nBravyi, and Terhal generalized this construction and proposed a method to construct topological subsystemncodes using 3-valent hypergraphs that satisfy certain constraints. Finding such hypergraphs and computing theirnparameters, however, is a nontrivial task.We propose families of topological subsystem codes that were previouslynnot known. In particular, our constructions give codes which cannot be derived from Bombin’s construction.nWe also study the error recovery schemes for the proposed subsystem codes and give detailed schedules for thensyndrome measurement that take advantage of the 2-locality of the gauge group. The study also leads to a newnand general construction for color codes.