Quantum error correction via codes over GF(4)
IEEE Transactions on Information Theory
Spatially correlated qubit errors and burst-correcting quantum codes
IEEE Transactions on Information Theory
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Most of the quantum error-correcting codes studied so far fall under the category of additive (or stabilizer) quantum codes, which are closely related to classical linear codes. The existence and general constructions of e_cient quantum codes that do not have such an underlying structure have remained elusive. Recently, specific examples of nonadditive quantum codes with minimum distance 2 have been presented. We, however, 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 - 2H2(2t/n), where H2(x) is the binary entropy function. In the process, we also develop a general set of sufficient conditions for a quantum code to be nonadditive. Finally, we introduce the notion of strongly nonadditive codes, and provide a construction for an ((11, 2, 3)) strongly nonadditive code.