Sparse Mamba Decoder for Quantum Error Correction: Efficient Defect-Centric Processing of Surface Code Syndromes

2026-05-16

AI Summary

This work addresses the computational redundancy in existing quantum error correction decoders, which process dense syndrome data even at low physical error rates. The authors propose a defect-centric sparse neural decoder that introduces a paradigm shift by exclusively handling active defect events. Leveraging the Mamba state-space model, the approach achieves linear-complexity inference while employing 13-dimensional defect features, sparse input processing, and ensemble learning to substantially reduce computational overhead on commodity GPUs. Experimental results demonstrate up to a 49% reduction in logical error rate and decoding speeds that are one to two orders of magnitude faster than state-of-the-art decoders, with consistent latency ranging from 24 to 57 microseconds.

Abstract

Quantum error correction (QEC) is essential for building fault-tolerant quantum computers, requiring decoders that are simultaneously accurate, fast, and scalable. Most state-of-the-art neural decoders achieve high accuracy but process the full dense syndrome array of size $O(d^2 R) $regardless of the actual error rate, where d is the code distance and R is the number of measurement rounds. At physically relevant error rates (p ~ 0.1%), fewer than 5% of syndrome entries contain active detection events -- yet existing decoders process the entire syndrome volume. We introduce the Sparse Mamba Decoder (SMD), a defect-centric neural decoder that processes only the k active detection events using a 13-dimensional feature representation per defect and a Mamba state-space backbone, achieving $O(k)$ complexity. Across depolarizing, uniform circuit-level, SI1000, and Google Sycamore experimental benchmarks, SMD reduces the MWPM logical error rate by up to 49% at $d \le 5$ under SI1000 noise, runs 95-467x faster than the Tesseract near-MLD decoder and 232-463x faster than Belief Matching, and maintains nearly constant latency (24-57 us) across d = 3-9 under uniform circuit-level noise. On the Sycamore experimental dataset, the SMD ensemble matches or slightly surpasses the dense Mamba decoder of Varbanov et al. All results are obtained on commodity NVIDIA GPUs with 7.5-16M parameters, without specialized accelerators.

Problem

• quantum error correction
• surface code
• syndrome decoding
• sparse processing
• defect-centric

Innovation

• Sparse Mamba Decoder
• defect-centric processing
• quantum error correction
• state-space model
• syndrome sparsity