Polylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channel
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 g...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Institute of Electrical and Electronics Engineers (IEEE)
2020
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| Online Access: | https://hdl.handle.net/1721.1/126678 |
| _version_ | 1826196910556315648 |
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| author | Lloyd, Seth Shor, Peter Williston Thompson, Kevin |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Lloyd, Seth Shor, Peter Williston Thompson, Kevin |
| author_sort | Lloyd, Seth |
| collection | MIT |
| description | 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). |
| first_indexed | 2024-09-23T10:39:54Z |
| format | Article |
| id | mit-1721.1/126678 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:39:54Z |
| publishDate | 2020 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1266782022-09-27T14:06:12Z Polylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channel Lloyd, Seth Shor, Peter Williston Thompson, Kevin Massachusetts Institute of Technology. Department of Mechanical Engineering Massachusetts Institute of Technology. Department of Mathematics 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). 2020-08-19T16:52:24Z 2020-08-19T16:52:24Z 2019-11 2018-07 2019-11-20T13:53:29Z Article http://purl.org/eprint/type/JournalArticle 1557-9654 0018-9448 https://hdl.handle.net/1721.1/126678 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. en 10.1109/TIT.2019.2925100 IEEE Transactions on Information Theory Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) arXiv |
| spellingShingle | Lloyd, Seth Shor, Peter Williston Thompson, Kevin Polylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channel |
| title | Polylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channel |
| title_full | Polylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channel |
| title_fullStr | Polylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channel |
| title_full_unstemmed | Polylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channel |
| title_short | Polylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channel |
| title_sort | polylog ldpc capacity achieving codes for the noisy quantum erasure channel |
| url | https://hdl.handle.net/1721.1/126678 |
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