2002/06/25 by V. Arvind, K. R. Parthasarathy, Arvind, V. +1
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0206174
16 pages, 2 figures
arxiv created 2002/06/25 · arxiv updated 2009/12/01
Using the Weyl commutation relations over a finite field we introduce a family of error-correcting quantum stabilizer codes based on a class of symmetric matrices over the finite field satisfying certain natural conditions. When the field is GF(2) the existence of a rich class of such symmetric matrices is demonstrated by a simple probabilistic argument depending on the Chernoff bound for i.i.d symmetric Bernoulli trials. If, in addition, these symmetric matrices are assumed to be circulant it is possible to obtain concrete examples by a computer program. The quantum codes thus obtained admit elegant encoding circuits.