1997/10/09 by Vwani Roychowdhury, Vwani P. Roychowdhury, Roychowdhury, Vwani P. +2
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9710031
21 pages
arxiv created 1997/10/09 · arxiv updated 2009/12/01
We first present a useful characterization of additive (stabilizer) quantum error-correcting codes. Then we present several examples of We first present a useful characterization of additive (stabilizer) quantum error--correcting codes. Then we present several examples of nonadditive codes. We show that there exist infinitely many non-trivial nonadditive codes with different minimum distances, and high rates. In fact, we show that nonadditive codes that correct t errors can reach the asymptotic rate R=1-2H(2t/n), where H(x) is the binary entropy function. Finally, we introduce the notion of strongly nonadditive codes (i.e., quantum codes with the following property: the trivial code consisting of the entire Hilbert space is the only additive code that is equivalent to any code containing the given code), and provide a construction for an ((11,2,3)) strongly nonadditive code.