Error‐Correction Code in Quantum Noise

Error‐correcting codes are the primary method of transmitting data in the classical world. The effects of contact with the atmosphere are expected to be so widespread in any quantum system utilized to do quantum learning and memory that quantum error correction will always be needed. Group theory is used extensively in both conventional and quantum error correction. For linear quantum error‐correcting codes, this chapter outlines a nonconstructive framework that specifies requirements for every code in the category. CSS codes (Calderbank‐Shor‐Steane), which belong to the larger category of stabilizer codes, have an advantage over other stabilizer codes since they may be built from pairs of classical codes that are coupled in a novel way. The chapter describes how to design a CSS code stabilizer. The stabilizer perspective is described as an alternative to the CSS code architecture described.