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Snowflake: A Distributed Streaming Decoder

Quantum Journal

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Researchers introduced a new quantum error correction decoder achieving 25% higher accuracy than the Union-Find decoder for surface codes under circuit-level noise, with subquadratic runtime scaling—improving on cubic scaling. The decoder operates in a streaming fashion, natively handling continuous error correction by processing data as it arrives, eliminating window overlap overhead found in existing methods. Its distributed, local architecture uses a grid of identical processing cells communicating only with nearest neighbors, enhancing speed, layout efficiency, and robustness in hardware implementation. Inspired by snowflake growth, the algorithm nucleates clusters at defects, merging them as they "fall" through time, simplifying error correction visualization and execution. Numerical results confirm superior performance in both accuracy and scalability, positioning it as a leading candidate for practical fault-tolerant quantum computing systems.

Snowflake: A Distributed Streaming Decoder

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AbstractWe design Snowflake, a quantum error correction decoder that, for the surface code under circuit-level noise, is roughly 25% more accurate than the Union-Find decoder, with a better mean runtime scaling: subquadratic as opposed to cubic in the code distance. Our decoder runs in a streaming fashion and has a distributed, local implementation. In designing Snowflake, we propose a new method for general stream decoding that eliminates the processing overhead due to window overlap in existing windowing methods.Featured image: An example of how Snowflake finds a correction (black lines), for two defects (red dots) separated in time (vertical axis) and space. Snowflake is explained by analogy to snowfall. As snowflakes fall they gradually grow; if two snowflakes touch they merge. In the same way, a cluster (green diamond) nucleates at each new defect at the top of the decoding window (square outline) and grows as it falls; if two clusters touch they merge.Popular summaryIt is widely believed quantum computers will be useful only if they are error corrected. A crucial part of error correction is the decoder: a classical algorithm that continuously deduces when errors have occurred from repeated measurements of the quantum processor. The decoder must be extremely fast and accurate. We design a decoder called Snowflake that is a streaming algorithm, so it natively handles the continuous nature of decoding. Snowflake is intended to run on hardware that is distributed and local i.e. a grid of identical processing cells, each communicating only with their nearest neighbours (this has practical benefits in speed, layout and robustness). Our numerics show that Snowflake is more accurate, and has a runtime that scales with distance more favourably, than a non-distributed implementation of an existing state-of-the-art decoder.► BibTeX data@article{Chan2026snowflake, doi = {10.22331/q-2026-03-20-2033}, url = {https://doi.org/10.22331/q-2026-03-20-2033}, title = {Snowflake: {A} {D}istributed {S}treaming {D}ecoder}, author = {Chan, Tim}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2033}, month = mar, year = {2026} }► References [1] D. J. Reilly. ``Challenges in scaling-up the control interface of a quantum computer''. In 2019 IEEE International Electron Devices Meeting (IEDM). Pages 31.7.1–31.7.6. (2019). https://doi.org/10.1109/IEDM19573.2019.8993497 [2] Poulami Das, Christopher A. Pattison, Srilatha Manne, Douglas M. Carmean, Krysta M. Svore, Moinuddin Qureshi, and Nicolas Delfosse. ``AFS: Accurate, fast, and scalable error-decoding for fault-tolerant quantum computers''. In 2022 IEEE International Symposium on High-Performance Computer Architecture (HPCA). Pages 259–273. (2022). https://doi.org/10.1109/HPCA53966.2022.00027 [3] Nicolas Delfosse, Andres Paz, Alexander Vaschillo, and Krysta M. Svore. ``How to choose a decoder for a fault-tolerant quantum computer? the speed vs accuracy trade-off'' (2023). arXiv:2310.15313. arXiv:2310.15313 [4] James William Harrington. ``Analysis of quantum error-correcting codes: symplectic lattice codes and toric codes''. PhD thesis. California Institute of Technology. (2004). https://doi.org/10.7907/AHMQ-EG82 [5] Austin G. Fowler. ``Minimum weight perfect matching of fault-tolerant topological quantum error correction in average $O(1)$ parallel time''. Quantum Information & Computation 15, 145–158 (2015). https://doi.org/10.26421/QIC15.1-2-9 [6] Michael Herold, Earl T. Campbell, Jens Eisert, and Michael J. Kastoryano. ``Cellular-automaton decoders for topological quantum memories''. npj Quantum Information 1, 15010 (2015). https://doi.org/10.1038/npjqi.2015.10 [7] Nikolas P. Breuckmann, Kasper Duivenvoorden, Dominik Michels, and Barbara M. Terhal. ``Local decoders for the 2D and 4D toric code''. Quantum Information & Computation 17, 181–208 (2017). https://doi.org/10.26421/QIC17.3-4-1 [8] Michael Herold, Michael J. Kastoryano, Earl T. Campbell, and Jens Eisert. ``Cellular automaton decoders of topological quantum memories in the fault tolerant setting''. New Journal of Physics 19, 063012 (2017). https://doi.org/10.1088/1367-2630/aa7099 [9] Nicolai Lang and Hans Peter Büchler. ``Strictly local one-dimensional topological quantum error correction with symmetry-constrained cellular automata''. SciPost Physics 4, 007 (2018). https://doi.org/10.21468/SciPostPhys.4.1.007 [10] Aleksander Kubica and John Preskill. ``Cellular-automaton decoders with provable thresholds for topological codes''.

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Campbell. ``Tangling schedules eases hardware connectivity requirements for quantum error correction''. PRX Quantum 5, 010348 (2024). https://doi.org/10.1103/PRXQuantum.5.010348 [71] Andrew Richards. ``University of Oxford Advanced Research Computing''. (2015). https://doi.org/10.5281/zenodo.22558 [72] David S. Wang, Austin G. Fowler, and Lloyd C. L. Hollenberg. ``Surface code quantum computing with error rates over 1%''. Physical Review A 83, 020302 (2011). https://doi.org/10.1103/PhysRevA.83.020302Cited byCould not fetch Crossref cited-by data during last attempt 2026-03-20 07:28:39: Could not fetch cited-by data for 10.22331/q-2026-03-20-2033 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-03-20 07:28:39: No response from ADS or unable to decode the received json data when getting the list of citing works.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractWe design Snowflake, a quantum error correction decoder that, for the surface code under circuit-level noise, is roughly 25% more accurate than the Union-Find decoder, with a better mean runtime scaling: subquadratic as opposed to cubic in the code distance. Our decoder runs in a streaming fashion and has a distributed, local implementation. In designing Snowflake, we propose a new method for general stream decoding that eliminates the processing overhead due to window overlap in existing windowing methods.Featured image: An example of how Snowflake finds a correction (black lines), for two defects (red dots) separated in time (vertical axis) and space. Snowflake is explained by analogy to snowfall. As snowflakes fall they gradually grow; if two snowflakes touch they merge. In the same way, a cluster (green diamond) nucleates at each new defect at the top of the decoding window (square outline) and grows as it falls; if two clusters touch they merge.Popular summaryIt is widely believed quantum computers will be useful only if they are error corrected. A crucial part of error correction is the decoder: a classical algorithm that continuously deduces when errors have occurred from repeated measurements of the quantum processor. The decoder must be extremely fast and accurate. We design a decoder called Snowflake that is a streaming algorithm, so it natively handles the continuous nature of decoding. Snowflake is intended to run on hardware that is distributed and local i.e. a grid of identical processing cells, each communicating only with their nearest neighbours (this has practical benefits in speed, layout and robustness). Our numerics show that Snowflake is more accurate, and has a runtime that scales with distance more favourably, than a non-distributed implementation of an existing state-of-the-art decoder.► BibTeX data@article{Chan2026snowflake, doi = {10.22331/q-2026-03-20-2033}, url = {https://doi.org/10.22331/q-2026-03-20-2033}, title = {Snowflake: {A} {D}istributed {S}treaming {D}ecoder}, author = {Chan, Tim}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2033}, month = mar, year = {2026} }► References [1] D. J. Reilly. ``Challenges in scaling-up the control interface of a quantum computer''. In 2019 IEEE International Electron Devices Meeting (IEDM). Pages 31.7.1–31.7.6. (2019). https://doi.org/10.1109/IEDM19573.2019.8993497 [2] Poulami Das, Christopher A. Pattison, Srilatha Manne, Douglas M. Carmean, Krysta M. Svore, Moinuddin Qureshi, and Nicolas Delfosse. ``AFS: Accurate, fast, and scalable error-decoding for fault-tolerant quantum computers''. In 2022 IEEE International Symposium on High-Performance Computer Architecture (HPCA). Pages 259–273. (2022). https://doi.org/10.1109/HPCA53966.2022.00027 [3] Nicolas Delfosse, Andres Paz, Alexander Vaschillo, and Krysta M. Svore. ``How to choose a decoder for a fault-tolerant quantum computer? the speed vs accuracy trade-off'' (2023). arXiv:2310.15313. arXiv:2310.15313 [4] James William Harrington. ``Analysis of quantum error-correcting codes: symplectic lattice codes and toric codes''. PhD thesis. California Institute of Technology. (2004). https://doi.org/10.7907/AHMQ-EG82 [5] Austin G. Fowler. ``Minimum weight perfect matching of fault-tolerant topological quantum error correction in average $O(1)$ parallel time''. Quantum Information & Computation 15, 145–158 (2015). https://doi.org/10.26421/QIC15.1-2-9 [6] Michael Herold, Earl T. Campbell, Jens Eisert, and Michael J. Kastoryano. ``Cellular-automaton decoders for topological quantum memories''. npj Quantum Information 1, 15010 (2015). https://doi.org/10.1038/npjqi.2015.10 [7] Nikolas P. Breuckmann, Kasper Duivenvoorden, Dominik Michels, and Barbara M. Terhal. ``Local decoders for the 2D and 4D toric code''. Quantum Information & Computation 17, 181–208 (2017). https://doi.org/10.26421/QIC17.3-4-1 [8] Michael Herold, Michael J. Kastoryano, Earl T. Campbell, and Jens Eisert. ``Cellular automaton decoders of topological quantum memories in the fault tolerant setting''. New Journal of Physics 19, 063012 (2017). https://doi.org/10.1088/1367-2630/aa7099 [9] Nicolai Lang and Hans Peter Büchler. ``Strictly local one-dimensional topological quantum error correction with symmetry-constrained cellular automata''. SciPost Physics 4, 007 (2018). https://doi.org/10.21468/SciPostPhys.4.1.007 [10] Aleksander Kubica and John Preskill. ``Cellular-automaton decoders with provable thresholds for topological codes''.

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Snowflake: A Distributed Streaming Decoder

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