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A p-bit parallel-tempering decoder in single-flux-quantum logic: simulated surface-code decoding below MWPM at 4 K

Year: 2026
Type: preprint
Abstract: We describe a decoder for the rotated surface code that runs as parallel tempering on probabilistic bits (p-bits) built from single-flux-quantum (SFQ) cells at 4.2 K. The X graph is decoded first, and its result switches the weights of the Z graph to account for X–Z correlations from Y errors. The p-bits, the edge toggle cells with merger trees for up to five writers and the timing of the colour clock are simulated at circuit level in JoSIM, and the measured properties enter a GPU model of the full decoder. Over d rounds of circuit-level noise at p = 0.006, paired shot by shot, the decoder has 14 to 18 % fewer logical failures than minimum-weight perfect matching (MWPM) at d = 5 and 27 to 36 % fewer at d = 7 (two independent seeds) and, with both seeds pooled, 2.2 % (d = 5) and 4.7 % (d = 7) more failures than correlated matching. Without the weight switching its logical outcome agrees with MWPM in almost every shot, so the gain comes from the X–Z correlation step (97 to 104 % of it); a deterministic two-stage control with the same switching rule comes within 2 % of correlated matching, so most of the remaining gap is due to the sampler. At p = 0.004 and 0.008 the decoder has 15 to 48 % fewer failures than MWPM (one seed). A block of d rounds is decoded in 0.53 µs (d = 5) and 1.67 µs (d = 7). Counted from the simulated cells, the core of the d = 7 decoder (p-bits, toggle cells, splitters, mergers; control logic and wiring excluded) needs 6.82 million Josephson junctions and 11 to 22 mW under energy-efficient RSFQ (ERSFQ) biasing. The decoder is a simulation study; it has not been built. Files. P5_manuscript.pdf: the manuscript. sfq_pbit_decoder_p5.tar.gz: simulation and analysis scripts (JoSIM test benches, GPU decoder model and its patches, evaluation scripts), JoSIM raw results, per-shot logical outcomes of all decoder runs, the receipts from which every number and figure is generated, the automated number checks and a self-test that reruns all evaluations and compares them field by field with the receipts. See README.md in the archive. Licences. Text and data CC BY 4.0, code MIT. Use of AI. Large language models (Claude, Anthropic) wrote most of the simulation and analysis code, ran the simulations, searched and read the literature, produced the figures and drafted the text under the author's direction; AI agents were also used as adversarial reviewers. Every number is generated by scripts from the raw simulation output and checked automatically.
DOI: 10.5281/zenodo.23323509
Language: English
Open Access status: green
OpenAlex ID: W7221510374
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