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High Performance Single-Error-Correcting Quantum Codes for Amplitude Damping

机译:用于幅度阻尼的高性能单错误校正量子码

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摘要

We construct families of high performance quantum amplitude damping codes. All of our codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension. One family is built from nonlinear error-correcting codes for classical asymmetric channels, with which we systematically construct quantum amplitude damping codes with parameters better than any prior construction known for any block length $ngeq 8$ except $n=2^{r}-1$ . We generalize this construction to employ classical codes over $GF(3)$ with which we numerically obtain better performing codes up to length 14. Because the resulting codes are of the codeword stabilized (CWS) type, conceptually simple (though potentially computationally expensive) encoding and decoding circuits are available.
机译:我们构造了一系列高性能的量子振幅阻尼码。我们所有的代码都是非加性的,在编码尺寸方面最适度地胜过了最佳的加性代码。一个族是由用于经典非对称信道的非线性纠错码构建而成的,利用该系统,我们可以系统地构造参数比任何已知的任何块长$ ngeq 8 $都更好的量子振幅阻尼码,除了$ n = 2 ^ {r}- 1 $。我们将这种构造推广为使用超过$ GF(3)$的经典代码,通过这些数字我们可以获得在长度上最大为14的性能更好的代码。因为生成的代码是码字稳定(CWS)类型的,所以从概念上讲是简单的(尽管可能在计算上很昂贵)编码和解码电路可用。

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