Sparse-Blossom Decoding in $o(1)$ Time

• URL: http://arxiv.org/abs/2609.12262v1
• Date: Thu, 10 Sep 2026 22:38:01 GMT
• Title: Sparse-Blossom Decoding in $o(1)$ Time
• Abstract summary: We show that a parallel sparse-blossom algorithm produces the same correction as the original, non-parallel sparse blossom.<n>These results provide a foundation for scalable parallel matching-based decoding.
• Score: 1.0742675209112622
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Matching-based decoding is widely used in quantum error correction, and accelerating it is key to enabling fast and scalable fault-tolerant quantum computation. Minimum-weight perfect matching (MWPM) decoding provides rigorous guarantees for error suppression, while sparse blossom enables its practical implementation at modest problem sizes. However, the runtime of existing sparse-blossom implementations unavoidably increases with problem size, motivating a rigorous parallelization framework that guarantees correctness and a runtime shorter than the syndrome-extraction timescale. Here, we present such a framework and prove that the resulting parallel sparse-blossom algorithm produces the same correction as the original, non-parallel sparse blossom. For the rotated surface code with code distance $d$ and physical error rates below a finite threshold, we prove that the average parallel runtime of decoding for $O(d)$ rounds of syndrome extraction is upper bounded by a quasi-polylogarithmic function of $d$. For a $d$-round decoding window, this implies that the average parallel runtime per round is $o(1)$. We also perform numerical simulation to identify conditions under which the parallel runtime per round decreases with increasing code distance. These results suggest that increasing code distance need not lead to longer parallel decoding times, providing a foundation for scalable parallel matching-based decoding.

Related papers

• dParallel: Learnable Parallel Decoding for dLLMs [77.24184219948337]
  Diffusion large language models (dLLMs) offer parallel token prediction and lower inference latency.<n>Existing open-source models still require nearly token-length decoding steps to ensure performance.<n>We introduce dParallel, a simple and effective method that unlocks the inherent parallelism of dLLMs for fast sampling.
  arXiv  Detail & Related papers  (2025-09-30T16:32:52Z)
• Learning to Parallel: Accelerating Diffusion Large Language Models via Learnable Parallel Decoding [21.609237262034636]
  Autoregressive decoding in large language models (LLMs) requires $mathcalO(n)$ sequential steps for $n$ tokens.<n>We propose Learning to Parallel Decode (Learn2PD), a framework that trains a lightweight and adaptive filter model to predict, for each token position, whether the current prediction matches the final output.<n>This learned filter approximates an oracle parallel decoding strategy that unmasks tokens only when correctly predicted.
  arXiv  Detail & Related papers  (2025-09-29T17:59:54Z)
• Fast correlated decoding of transversal logical algorithms [67.01652927671279]
  Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead.<n>Recent advances have shown that by jointly decoding logical qubits in algorithms composed of logical gates, the number of syndrome extraction rounds can be reduced.<n>Here, we reform the problem of decoding circuits by directly decoding relevant logical operator products as they propagate through the circuit.
  arXiv  Detail & Related papers  (2025-05-19T18:00:00Z)
• Hardware-Aware Parallel Prompt Decoding for Memory-Efficient Acceleration of LLM Inference [23.633481089469836]
  Auto-regressive decoding of Large Language Models (LLMs) results in significant overheads in their hardware performance.<n>We propose a novel parallel prompt decoding that requires only $0.0002$% trainable parameters, enabling efficient training on a single A100-40GB GPU in just 16 hours.<n>Our approach demonstrates up to 2.49$times$ speedup and maintains a minimal memory overhead of just $0.0004$%.
  arXiv  Detail & Related papers  (2024-05-28T22:19:30Z)
• FPGA-based Distributed Union-Find Decoder for Surface Codes [3.780617572622938]
  A fault-tolerant quantum computer must decode and correct errors faster than they appear to prevent exponential slowdown due to error correction. We report a distributed version of the Union-Find decoder that exploits parallel computing resources for further speedup.
  arXiv  Detail & Related papers  (2024-03-20T13:36:59Z)
• Fast Chain-of-Thought: A Glance of Future from Parallel Decoding Leads to Answers Faster [61.83949316226113]
  FastCoT is a model-agnostic framework based on parallel decoding. We show that FastCoT saves inference time by nearly 20% with only a negligible performance drop compared to the regular approach.
  arXiv  Detail & Related papers  (2023-11-14T15:56:18Z)
• Scalable Quantum Error Correction for Surface Codes using FPGA [67.74017895815125]
  A fault-tolerant quantum computer must decode and correct errors faster than they appear. We report a distributed version of the Union-Find decoder that exploits parallel computing resources for further speedup. The implementation employs a scalable architecture called Helios that organizes parallel computing resources into a hybrid tree-grid structure.
  arXiv  Detail & Related papers  (2023-01-20T04:23:00Z)
• Scalable surface code decoders with parallelization in time [8.28402656078529]
  We introduce a sliding-window decoding scheme that provides fast classical processing for the surface code through parallelism. Our scheme divides the syndromes in spacetime into overlapping windows along the time direction, which can be decoded in parallel with any inner decoder.
  arXiv  Detail & Related papers  (2022-09-19T17:42:53Z)
• Rapid Person Re-Identification via Sub-space Consistency Regularization [51.76876061721556]
  Person Re-Identification (ReID) matches pedestrians across disjoint cameras. Existing ReID methods adopting real-value feature descriptors have achieved high accuracy, but they are low in efficiency due to the slow Euclidean distance computation. We propose a novel Sub-space Consistency Regularization (SCR) algorithm that can speed up the ReID procedure by 0.25$ times.
  arXiv  Detail & Related papers  (2022-07-13T02:44:05Z)
• A Push-Relabel Based Additive Approximation for Optimal Transport [5.111364864495785]
  Exact algorithms for computing Optimal Transport can be slow. We introduce a new and very simple approach to find an $varepsilon$approximation of the OT distance. Our algorithm achieves a near-optimal execution time of $O(n2/varepsilon2)$ for computing OT distance.
  arXiv  Detail & Related papers  (2022-03-07T21:40:14Z)
• Accelerating Feedforward Computation via Parallel Nonlinear Equation Solving [106.63673243937492]
  Feedforward computation, such as evaluating a neural network or sampling from an autoregressive model, is ubiquitous in machine learning. We frame the task of feedforward computation as solving a system of nonlinear equations. We then propose to find the solution using a Jacobi or Gauss-Seidel fixed-point method, as well as hybrid methods of both. Our method is guaranteed to give exactly the same values as the original feedforward computation with a reduced (or equal) number of parallelizable iterations, and hence reduced time given sufficient parallel computing power.
  arXiv  Detail & Related papers  (2020-02-10T10:11:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.