ar X iv : q ua nt - p h / 97 03 04 8 v 1 2 5 M ar 1 99 7 NONBINARY QUANTUM CODES

Abstract

We present several results on quantum codes over general alphabets (that is, in which the fundamental units may have more than 2 states). In particular, we consider codes derived from finite symplectic geometry assumed to have additional global symmetries. From this standpoint, the analogues 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 analogues of quadratic residue codes, including a singleerror 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.

Cite this paper

@inproceedings{Rains2007arXI, title={ar X iv : q ua nt - p h / 97 03 04 8 v 1 2 5 M ar 1 99 7 NONBINARY QUANTUM CODES}, author={Eric M. Rains}, year={2007} }