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arXiv · 1703.00382

polylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channel

Seth Lloyd·Peter Shor·Kevin Thompson
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Abstract

We provide $poly\log$ sparse quantum codes for correcting the erasure channel arbitrarily close to the capacity. Specifically, we provide $[[n, k, d]]$ 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 $\langle S_1, S_2, ... S_{n-k} \rangle$ such that $|S_i|\leq \log^{2+\zeta}(n)$ for all $i$ and for any $\zeta > 0$ with high probability. In this work we show that the result of Delfosse et al. is tight: one can construct capacity approaching codes with weight almost $O(1)$.

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Seth Lloyd, Peter Shor, Kevin Thompson. 2017-03-01. polylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channel. https://arxiv.org/abs/1703.00382

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