Quantum LDPC Codes With Almost Linear Minimum Distance

Panteleev, Pavel; Kalachev, Gleb

doi:10.1109/tit.2021.3119384

Cited by 66 publications

(66 citation statements)

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“…For a QLDPC code on n qubits with m stabilizers the matrix H is an m × 2n binary matrix 2. Since the first version of the current work was released, the codes from this family have been shown to have very large minimal distances[16,17,18] and found interesting applications in geometry[19]. In[17] they were further generalized and called lifted product codes.…”

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confidence: 99%

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Degenerate Quantum LDPC Codes With Good Finite Length Performance

Panteleev

Kalachev

2021

Quantum

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We study the performance of medium-length quantum LDPC (QLDPC) codes in the depolarizing channel. Only degenerate codes with the maximal stabilizer weight much smaller than their minimum distance are considered. It is shown that with the help of OSD-like post-processing the performance of the standard belief propagation (BP) decoder on many QLDPC codes can be improved by several orders of magnitude. Using this new BP-OSD decoder we study the performance of several known classes of degenerate QLDPC codes including hypergraph product codes, hyperbicycle codes, homological product codes, and Haah's cubic codes. We also construct several interesting examples of short generalized bicycle codes. Some of them have an additional property that their syndromes are protected by small BCH codes, which may be useful for the fault-tolerant syndrome measurement. We also propose a new large family of QLDPC codes that contains the class of hypergraph product codes, where one of the used parity-check matrices is square. It is shown that in some cases such codes have better performance than hypergraph product codes. Finally, we demonstrate that the performance of the proposed BP-OSD decoder for some of the constructed codes is better than for a relatively large surface code decoded by a near-optimal decoder.

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confidence: 99%

“…Since the first version of this work appeared in arXiv, some lower bounds on the minimal distance have been obtained in[16,17,18] for special cases of QC GHP codes C(A, 1 + x).…”

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confidence: 99%

Degenerate Quantum LDPC Codes With Good Finite Length Performance

Panteleev

Kalachev

2021

Quantum

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“…After two decades, [EKZ20] broke the √ N barrier and there was a flurry of activity with [HHO21] extending it to N 3/5 (up to poly log factors). Panteleev and Kalachev [PK21b] came up with another breakthrough construction achieving almost linear distance. Both [HHO21] and [PK21b] are non-explicit constructions crucially relying on symmetries.…”

Section: Introductionmentioning

confidence: 99%

“…Panteleev and Kalachev [PK21b] came up with another breakthrough construction achieving almost linear distance. Both [HHO21] and [PK21b] are non-explicit constructions crucially relying on symmetries. The construction in [PK21b] interestingly used quasi-cyclic LDPC codes which in turn was constructed using expander graphs with cyclic symmetry.…”

Section: Introductionmentioning

confidence: 99%

“…Both [HHO21] and [PK21b] are non-explicit constructions crucially relying on symmetries. The construction in [PK21b] interestingly used quasi-cyclic LDPC codes which in turn was constructed using expander graphs with cyclic symmetry. Moreover, Breuckmann and Eberhardt [BE21] introduced a new approach for constructing quantum codes simultaneously generalizing [HHO21] and [PK21b] in order to obtain explicit codes out of a pair of graphs having the symmetries of any group.…”

Section: Introductionmentioning

confidence: 99%

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