Polylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channel
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1703.00382.pdf
Description
Submitted version
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506.76 KB
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Checksum (MD5)
02568eb8d911e2eafaa9a24867e9d82f
Author(s)
Lloyd, Seth
Shor, Peter Williston
Thompson, Kevin
Date Issued
November 2019
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
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.
Version
Original manuscript
Abstract
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. [5] is tight: one can construct capacity approaching codes with weight almost O(1).
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1109/TIT.2019.2925100
