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01640nam a2200205Ia 4500 |
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10.3390-sym14071348 |
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220718s2022 CNT 000 0 und d |
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|a 20738994 (ISSN)
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| 245 |
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|a Distance Bounds for Generalized Bicycle Codes
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| 260 |
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|b MDPI
|c 2022
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| 856 |
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|z View Fulltext in Publisher
|u https://doi.org/10.3390/sym14071348
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|a Generalized bicycle (GB) codes is a class of quantum error-correcting codes constructed from a pair of binary circulant matrices. Unlike for other simple quantum code ansätze, unrestricted GB codes may have linear distance scaling. In addition, low-density parity-check GB codes have a naturally overcomplete set of low-weight stabilizer generators, which is expected to improve their performance in the presence of syndrome measurement errors. For such GB codes with a given maximum generator weight w, we constructed upper distance bounds by mapping them to codes local in D ≤ w − 1 dimensions, and lower existence bounds which give d ≥ O(n1/2). We have also conducted an exhaustive enumeration of GB codes for certain prime circulant sizes in a family of two-qubit encoding codes with row weights 4, 6, and 8; the observed distance scaling is consistent with A(w)n1/2 + B(w), where n is the code length and A(w) is increasing with w. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
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|a distance bounds
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|a generalized bicycle codes
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|a quantum error-correcting codes
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|a quantum LDPC codes
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|a stabilizer codes
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|a Pryadko, L.P.
|e author
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|a Wang, R.
|e author
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| 773 |
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|t Symmetry
|x 20738994 (ISSN)
|g 14 7
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