Gauge Structures: From Stabilizer Codes to Continuum Models

Understand

Stabilizer codes are a powerful method for implementing fault-tolerant quantum memory and in the case of topological codes, they form useful models for topological phases of matter.

• In this paper, we discuss the theory of stabilizer codes as a discrete version of a linear gauge structure, a concept we introduce here.
• A linear gauge structure captures all the familiar ingredients of $U(1)$ gauge theory including a generalization of charge conservation, Maxwell equations and topological terms.
• Using this connection, we prove some important results for stabilizer codes which can be used to characterize their error-correction properties.