Compare Papers

Paper 1

FPGA-tailored algorithms for real-time decoding of quantum LDPC codes

Satvik Maurya, Thilo Maurer, Markus Bühler, Drew Vandeth, Michael E. Beverland

Year

2025

Journal

arXiv preprint

DOI

arXiv:2511.21660

arXiv

2511.21660

Real-time decoding is crucial for fault-tolerant quantum computing but likely requires specialized hardware such as field-programmable gate arrays (FPGAs), whose parallelism can alter relative algorithmic performance. We analyze FPGA-tailored versions of three decoder classes for quantum low-density parity-check (qLDPC) codes: message passing, ordered statistics, and clustering. For message passing, we analyze the recently introduced Relay decoder and its FPGA implementation; for ordered statistics decoding (OSD), we introduce a filtered variant that concentrates computation on high-likelihood fault locations; and for clustering, we design an FPGA-adapted generalized union-find decoder. We design a systolic algorithm for Gaussian elimination on rank-deficient systems that runs in linear parallel time, enabling fast validity checks and local corrections in clustering and eliminating costly full-rank inversion in filtered-OSD. Despite these improvements, both remain far slower and less accurate than Relay, suggesting message passing is the most viable route to real-time qLDPC decoding.

Open paper

Paper 2

Tradeoffs on the volume of fault-tolerant circuits

Anirudh Krishna, Gilles Zémor

Year

2025

Journal

arXiv preprint

DOI

arXiv:2510.03057

arXiv

2510.03057

Dating back to the seminal work of von Neumann [von Neumann, Automata Studies, 1956], it is known that error correcting codes can overcome faulty circuit components to enable robust computation. Choosing an appropriate code is non-trivial as it must balance several requirements. Increasing the rate of the code reduces the relative number of redundant bits used in the fault-tolerant circuit, while increasing the distance of the code ensures robustness against faults. If the rate and distance were the only concerns, we could use asymptotically optimal codes as is done in communication settings. However, choosing a code for computation is challenging due to an additional requirement: The code needs to facilitate accessibility of encoded information to enable computation on encoded data. This seems to conflict with having large rate and distance. We prove that this is indeed the case, namely that a code family cannot simultaneously have constant rate, growing distance and short-depth gadgets to perform encoded CNOT gates. As a consequence, achieving good rate and distance may necessarily entail accepting very deep circuits, an undesirable trade-off in certain architectures and applications.

Open paper