Stabilizer Codes for Continuous-variable Quantum Error Correction

Abstract

A generalization of the stabilizer code construction presented by Gottesman is described, which allows for the construction of quantum error-correcting codes for continuous-variable systems. This formalism describes all continuous-variable codes presented to date, and can be used to construct new codes based on discrete-variable codes or classical codes. We use it to describe the nine-mode code given by Lloyd and Slotine, and a five-mode code described by Braunstein. In addition, we construct a new continuous-variable code based an code of Gottesman which encodes three logical modes of information into eight physical modes and corrects one error. This generalization is a step toward an independent understanding of continuous-variable quantum information and a theory of fault-tolerant quantum information processing.