University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Faculty Publications, Department of Physics and Research Papers in Physics and Astronomy Astronomy 2014 Parafermion stabilizer codes Utkan Güngördü University of Nebraska-Lincoln,
[email protected] Rabindra Nepal University of Nebraska-Lincoln,
[email protected] Alexey Kovalev University of Nebraska - Lncoln,
[email protected] Follow this and additional works at: http://digitalcommons.unl.edu/physicsfacpub Part of the Quantum Physics Commons Güngördü, Utkan; Nepal, Rabindra; and Kovalev, Alexey, "Parafermion stabilizer codes" (2014). Faculty Publications, Department of Physics and Astronomy. 131. http://digitalcommons.unl.edu/physicsfacpub/131 This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Faculty Publications, Department of Physics and Astronomy by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. PHYSICAL REVIEW A 90, 042326 (2014) Parafermion stabilizer codes Utkan Gung¨ ord¨ u,¨ Rabindra Nepal, and Alexey A. Kovalev Department of Physics and Astronomy and Nebraska Center for Materials and Nanoscience, University of Nebraska, Lincoln, Nebraska 68588, USA (Received 23 September 2014; published 21 October 2014) We define and study parafermion stabilizer codes, which can be viewed as generalizations of Kitaev’s one- dimensional (1D) model of unpaired Majorana fermions. Parafermion stabilizer codes can protect against low- weight errors acting on a small subset of parafermion modes in analogy to qudit stabilizer codes. Examples of several smallest parafermion stabilizer codes are given. A locality-preserving embedding of qudit operators into parafermion operators is established that allows one to map known qudit stabilizer codes to parafermion codes.