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Nonbinary quantum codes

Rains, Eric M. (1999) Nonbinary quantum codes. IEEE Transactions on Information Theory, 45 (6). pp. 1827-1832. ISSN 0018-9448. doi:10.1109/18.782103.

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We present several results on quantum codes over general alphabets (that is, in which the fundamental units may have more than two states). In particular, we consider codes derived from finite symplectic geometry assumed to have additional global symmetries. From this standpoint, the analogs of Calderbank-Shor-Steane codes and of GF(4)-linear codes turn out to be special cases of the same construction. This allows us to construct families of quantum codes from certain codes over number fields; in particular, we get analogs of quadratic residue codes, including a single-error-correcting code encoding one letter in five, for any alphabet size. We also consider the problem of fault-tolerant computation through such codes, generalizing ideas of Gottesman (see Phys. Rev. A, vol.57, no.1, p127-37, 1998).

Item Type:Article
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Additional Information:© 1999 IEEE. Manuscript received March 25, 1997; revised February 1, 1999.
Subject Keywords:Finite fields, quantum codes, symplectic
Issue or Number:6
Record Number:CaltechAUTHORS:20170926-145137075
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Official Citation:E. M. Rains, "Nonbinary quantum codes," in IEEE Transactions on Information Theory, vol. 45, no. 6, pp. 1827-1832, Sep 1999. doi: 10.1109/18.782103 URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81849
Deposited By: Tony Diaz
Deposited On:26 Sep 2017 22:42
Last Modified:15 Nov 2021 19:46

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