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Abstract: Quantum error control codes allow to detect and correct errors that are due to decoherence effects. We review some basic properties of these codes and give some constructions. Our main focus will be on a construction of quantum error control codes that have been introduced by Knill in 1996 with the intention to generalize stabilizer codes. These so-called Clifford codes can be constructed and analyzed with tools from representation theory of finite groups. We show that a large class of Clifford ... (Update)
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BibTeX entry: (Update)
@misc{ klappenecker-clifford,
author = "Andreas Klappenecker and Martin Rötteler",
title = "Clifford Codes",
url = "citeseer.ist.psu.edu/454319.html" }
Citations (may not include all citations):52 Good quantum error-correcting codes exist - Calderbank, Shor - 1996
47 Mixed state entanglement and quantum error correction (context) - Bennett, DiVincenzo et al. - 1996
45 Fault-tolerant quantum computation - Shor - 1996
42 Multiple-particle interference and quantum error correction (context) - Steane - 1996
37 Quantum error correction and orthogonal geometry (context) - Calderbank, Rains et al. - 1997
36 A theory of quantum error{correcting codes - Knill, amme - 1997
35 Quantum error correction via codes over GF - Calderbank, Rains et al. - 1998
34 Class of quantum error-correcting codes saturating the quant.. (context) - Gottesman - 1996
33 Fault-tolerant quantum computation with constant error - Aharonov, Ben-Or - 1997
19 Character Theory of Finite Groups (context) - Isaacs - 1976
19 Scheme for reducing decoherence in quantum memory (context) - Shor - 1995
15 Simple quantum error correcting codes (context) - Steane - 1996
9 A Course on Group Theory (context) - Rose - 1994
6 Nonbinary quantum codes (context) - Rains - 1999
4 Theory of quantum error correction for general noise (context) - Knill, amme et al. - 2000
3 Quantum error detection I: Statement of the problem - Ashikhmin, Barg et al. - 2000
3 Quantum error detection II: Bounds - Ashikhmin, Barg et al. - 2000
3 Ecient computations of encodings for quantum error correctio.. (context) - Cleve, Gottesman - 1997
2 Beyond stabilizer codes (context) - Klappenecker, otteler - 2000
2 A remark on unitary error bases (context) - Klappenecker, otteler - 2000
2 Representations induced in an invariant subgroup (context) - Cli - 1937
2 Los Alamos National Laboratory Report LAUR (context) - Knill, error et al. - 1996
2 Stabilizing quantum information (context) - Zanardi - 2001
1 Algorithmic aspects of error-correcting codes (context) - Grassl - 2001
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