Nonbinary quantum codes

Details Nonbinary quantum codes Nonbinary quantum codes

1997-03-25

arxiv.org/abs/quant-ph/9703048v1

Physics

Quantum Physics

11 pages, AMSTeX

Scientific paper

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 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.

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