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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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Electrical and Electronics Engineers (IEEE)
2020
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| Online Access: | https://hdl.handle.net/1721.1/126678 |
| Summary: | 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). |
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