51. Polylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channel.
- Author
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Lloyd, Seth, Shor, Peter, and Thompson, Kevin
- Subjects
- *
BINARY codes , *CIPHERS , *QUANTUM computing , *ERROR correction (Information theory) , *QUANTUM mechanics - Abstract
We provide polylog sparse quantum codes for correcting the Erasure channel arbitrarily close to the capacity. Specifically, we provide the $[[n, k, d]]$ quantum stabilizer codes that correct for the erasure channel arbitrarily close to the capacity if the erasure probability is at least 0.33 and with a generating set $\langle S_{1}, S_{2}, \cdots {} S_{n-k} \rangle $ such that $|S_{i}|\leq {\mathrm{ log}} ^{2+\zeta }(n)$ for all $i$ and for any $\zeta > 0$ with high probability. In this paper, we show that the result of Delfosse et al. is tight: one can construct capacity approaching codes with weight almost $O(1)$. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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