Polylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channel
Seth Lloyd, Peter W. Shor, Kevin Thompson · IEEE Transactions on Information Theory · 2019
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 (S1, S2, ... Sn-k) such that |Si| ≤ log2+ζ(n) for all i and for any ζ > 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).