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An efficient decoder for a linear distance quantum LDPC code
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Recent developments have shown the existence of quantum low-density parity check (qLDPC) codes with constant rate and linear distance. A natural question concerns the efficient decodability of these codes. In this paper, we present a linear time decoder for the recent quantum Tanner codes construction of asymptotically good qLDPC codes, which can correct all errors of weight up to a constant fraction of the blocklength. Our decoder is an iterative algorithm which searches for corrections within constant-sized regions. At each step, the corrections are found by reducing a locally defined and efficiently computable cost function which serves as a proxy for the weight of the remaining error.
Forward citations
Cited by 3 Pith papers
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Classifying Logical Gates in Quantum Codes via Cohomology Operations and Symmetry
Cohomology operations, including new higher Pontryagin powers, yield constant-depth logical R_k and multi-controlled R_k gates in homological quantum codes on projective spaces, extending the known color-code paradigm.
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Multivariate Multicycle Codes for Complete Single-Shot Decoding
Koszul complexes built from four polynomial generators over cyclic group rings yield CSS codes with both X and Z metachecks, giving small, high-confinement, single-shot-decodable quantum codes.
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Quantum Tanner Codes at Moderate Blocklength
A search over non-abelian groups yields new moderate-blocklength quantum Tanner code instances whose randomized distance bounds exceed 20, with decoder pseudo-thresholds comparable to shorter codes.
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