Polylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channel
Author(s)Lloyd, Seth; Shor, Peter Williston; Thompson, Kevin
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We provide polylog 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 hS1, S2, . . . Sn−ki such that |Si | ≤ log2+ζ (n) for all i and for any ζ > 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).
DepartmentMassachusetts Institute of Technology. Department of Mechanical Engineering; Massachusetts Institute of Technology. Department of Mathematics
IEEE Transactions on Information Theory
Institute of Electrical and Electronics Engineers (IEEE)
S. Lloyd, P. Shor and K. Thompson, "Polylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channel," in IEEE Transactions on Information Theory, vol. 65, no. 11, pp. 7584-7595, Nov. 2019, doi: 10.1109/TIT.2019.2925100.