A Finite Gilbert–Varshamov Bound for Pure Stabilizer Quantum Codes

Feng, Keqin; Ma, Zhi

doi:10.1109/tit.2004.838088

Cited by 106 publications

(88 citation statements)

References 5 publications

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“…It is easy to check that the reverse mapping also works. Note that an original code that exceeds the generic quantum Gilbert-Varshamov (GV) bound [35] is mapped to a CSS code that exceeds the version of the GV bound specific for such codes [33]. Also, an original sparse code is mapped to a sparse code, with the same limit on the column weight, and row weight at most doubled.…”

Section: Theorem 1 For Any Quantum Stabilizer Code [[Nkd]] With Thmentioning

confidence: 99%

Quantum Kronecker sum-product low-density parity-check codes with finite rate

Kovalev

Pryadko

2013

Phys. Rev. A

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We introduce an ansatz for quantum codes which gives the hypergraph-product (generalized toric) codes by Tillich and Zémor and generalized bicycle codes by MacKay et al. as limiting cases. The construction allows for both the lower and the upper bounds on the minimum distance; they scale as a square root of the block length. Many thus defined codes have a finite rate and limited-weight stabilizer generators, an analog of classical low-density parity-check (LDPC) codes. Compared to the hypergraph-product codes, hyperbicycle codes generally have a wider range of parameters; in particular, they can have a higher rate while preserving the estimated error threshold.

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Section: Theorem 1 For Any Quantum Stabilizer Code [[Nkd]] With Thmentioning

confidence: 99%

Quantum Kronecker sum-product low-density parity-check codes with finite rate

Kovalev

Pryadko

2013

Phys. Rev. A

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“…16 and 17 on L-chains and Corollary 3.1, we can also construct some new quantum codes of minimum distance 5. 17 There are the following L-chains: [14,8,5] ⊆ [14,13,2], [16,9,5] ⊆ [16,15,2], [18,12,5] ⊆ [18,17,2], [20,13,5] …”

Section: New Quantum Codesmentioning

confidence: 99%

Combinatorial Construction of Linear Quantum Codes From Quaternary BCH Codes

Zhao

2009

Int. J. Quantum Inform.

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Classical BCH codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes. But for given restricted length n, good quantum BCH codes are very sparse. In this paper, by puncturing and pasting check matrices of Hermitian dual containing BCH codes over the quaternary field, we construct many linear quantum codes with good parameters, and some of them have parameters exceeding the finite Gilbert-Varshamov bound for stabilizer quantum codes.

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“…The quantum Hamming bound states (see [20,22]) that: Any pure ((n, K, d)) q stabilizer code satisfies…”

Section: Bounds On Quantum Codesmentioning

confidence: 99%