Sparse-graph codes for quantum error correction

By David John Cameron MacKay, Graeme J. Mitchison, P. L. Mcfadden. IEEE Transactions on Information Theory, 2003

411 citations recorded by the source corpus.

Sparse-graph codes appropriate for use in quantum error-correction are presented. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based on sparse graphs. Second, sparse-graph codes keep the number of quantum interactions associated with the quantum error-correction process small: a constant number per quantum bit, independent of the block length. Third, sparse-graph codes often offer great flexibility with respect to block length and rate. We believe some of the codes we present are unsurpassed by previously published quantum error-correcting codes.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/4b14c7ec0724440993f38189946f80cf40ff9b8d

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Citations in the corpus

Nonbinary Stabilizer Codes Over Finite Fields (2005, methodology): “We selected code families that are easily accessible by elementary methods; the interested reader can ﬁnd examples of more intricate algebro-geometric constructions in [6], [25], [26], [57], [70] and of binary quantum LDPC codes in [21], [66], [77].”
Applications of LDPC Codes to the Wiretap Channel (2004, neutral): “Since|S| = |v+S|, the number of vectors consistent withz in each consistent coset is a constant equal to the size of the set on the RHS above.”
Asymptotically good Quantum and locally testable classical LDPC codes (2021, methodology): “In this work, we consider several new families of classical and quantum LDPC codes of constant rate based on the introduced recently lifted product construction [44], which generalizes many known constructions of quantum LDPC codes [24, 25, 34, 38, 49, 52].”
Degenerate Quantum LDPC Codes With Good Finite Length Performance (2019, background): “The corresponding class of codes is called the generalized bicycle (GB) codes, where the bicycle codes [37] are obtained as a special case when B = AT.”
High-threshold and low-overhead fault-tolerant quantum memory (2023, methodology): “Our codes are a generalization of bicycle codes proposed by MacKay et al. 41 and studied in more depth in refs.”