Codeword Stabilized Quantum Codes

• Published in: IEEE transactions on information theory Vol. 55; no. 1; pp. 433 - 438
• Main Authors: Cross, A., Smith, G., Smolin, J.A., Bei Zeng
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-01-2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additives; Applied sciences; Boolean functions; Circuit simulation; Circuits; Codes; Coding, codes; Computational modeling; Computer simulation; Construction; Corrections; Councils; Design; Eigenvalues and eigenfunctions; Encoding; Error correcting codes; Error correction codes; Errors; Exact sciences and technology; Fault tolerance; Information theory; Information, signal and communications theory; Nonadditive codes; Quantum computing; quantum error correction; Signal and communications theory; stabilizer codes; Telecommunications and information theory; stabilizer codes; Nonadditive codes; Error correcting code; Error correction; Coding; quantum error correction
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2008.2008136

We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with superior parameters to any previously known. In particular, we find ((10,18,3)) and ((10,20,3)) codes. We also show how to construct encoding circuits for all codes within our framework.