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dc.contributor.authorLloyd, Seth
dc.contributor.authorShor, Peter Williston
dc.contributor.authorThompson, Kevin
dc.date.accessioned2020-08-19T16:52:24Z
dc.date.available2020-08-19T16:52:24Z
dc.date.issued2019-11
dc.date.submitted2018-07
dc.identifier.issn1557-9654
dc.identifier.issn0018-9448
dc.identifier.urihttps://hdl.handle.net/1721.1/126678
dc.description.abstractWe 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).en_US
dc.language.isoen
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en_US
dc.relation.isversionof10.1109/TIT.2019.2925100en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titlePolylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channelen_US
dc.typeArticleen_US
dc.identifier.citationS. 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.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mechanical Engineeringen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.relation.journalIEEE Transactions on Information Theoryen_US
dc.eprint.versionOriginal manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dc.date.updated2019-11-20T13:53:29Z
dspace.date.submission2019-11-20T13:53:33Z
mit.journal.volume65en_US
mit.journal.issue11en_US


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