FPGA-tailored algorithms for real-time decoding of quantum LDPC codes
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912847974367232 |
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| author | Maurya, Satvik Maurer, Thilo Bühler, Markus Vandeth, Drew Beverland, Michael E. |
| author_facet | Maurya, Satvik Maurer, Thilo Bühler, Markus Vandeth, Drew Beverland, Michael E. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21660 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | FPGA-tailored algorithms for real-time decoding of quantum LDPC codes Maurya, Satvik Maurer, Thilo Bühler, Markus Vandeth, Drew Beverland, Michael E. Quantum Physics 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. |
| title | FPGA-tailored algorithms for real-time decoding of quantum LDPC codes |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2511.21660 |