Advancing Finite-Length Quantum Error Correction Using Generalized Bicycle Codes
Olai Å. Mostad, Hsuan-Yin Lin, Eirik Rosnes, De-Shih Lee, Ching-Yi Lai
TL;DR
This work evaluates generalized bicycle (GB) quantum codes for finite-length error correction, highlighting their flexibility to achieve high rates and good distance under practical decoding. By deploying two constructive schemes, $MMM$ and $PK$, GB codes are tailored to specific length, rate, and row-weight constraints and decoded with a memory belief propagation framework plus approximate degenerate ordered statistics decoding. Across multiple benchmarks, GB codes show competitive or superior performance to quantum Tanner codes, single-parity-check product codes, and bivariate bicycle codes at comparable lengths, with particularly strong results when row weights are increased or unrestricted. The findings demonstrate GB codes as a practical, adaptable option for near-term quantum error correction, while also revealing trade-offs with decoding complexity and fault-tolerant syndrome extraction in higher-weight regimes.
Abstract
Generalized bicycle (GB) codes have emerged as a promising class of quantum error-correcting codes with practical decoding capabilities. While numerous asymptotically good quantum codes and quantum low-density parity-check code constructions have been proposed, their finite block-length performance often remains unquantified. In this work, we demonstrate that GB codes exhibit comparable or superior error correction performance in finite-length settings, particularly when designed with higher or unrestricted row weights. Leveraging their flexible construction, GB codes can be tailored to achieve high rates while maintaining efficient decoding. We evaluate GB codes against other leading quantum code families, such as quantum Tanner codes and single-parity-check product codes, highlighting their versatility in practical finite-length applications.