sparse-mamba-decoder-qec

name	sparse-mamba-decoder-qec
description	Sparse Mamba Decoder (SMD) for quantum error correction — a defect-centric neural decoder using Mamba state-space model that processes only active detection events (k ≪ d²R) achieving O(k) complexity on surface codes. 95-467x faster than Tesseract near-MLD decoder.
version	1.0.0
author	Hermes Agent (Cron Job)
license	MIT

Sparse Mamba Decoder (SMD) for Quantum Error Correction

arXiv: 2605.17156 (May 2026) Authors: Samira Sayedsalehi, Nader Bagherzadeh, Maxim Shcherbakov, Jean-Luc Gaudiot

Overview

The Sparse Mamba Decoder (SMD) is a defect-centric neural decoder for surface-code quantum error correction. Unlike existing neural decoders that process the full dense syndrome array (O(d²R) complexity), SMD processes only the k active detection events using a Mamba state-space backbone, achieving O(k) complexity.

Key Innovation

At physically relevant error rates (p ~ 0.1%), fewer than 5% of syndrome entries contain active detection events. SMD exploits this sparsity by encoding each defect with a 13-dimensional feature representation and processing them through a Mamba (structured state-space) model, enabling nearly constant latency across code distances.

Core Methodology

1. Defect-Centric Processing

• Instead of processing the full d²R syndrome volume, SMD identifies only active detection events
• Each active event is encoded as a 13-dimensional feature vector (spatial position, round, neighbors, etc.)
• Number of active events k ≪ d²R at low error rates

2. Mamba State-Space Backbone

• Uses the Mamba architecture (SSM-based, linear complexity in sequence length)
• Processes the variable-length sequence of defect features
• Outputs correction predictions

3. SMD Ensemble

• Multiple SMD decoders can be combined in an ensemble for improved accuracy
• On Sycamore experimental data, matches or slightly surpasses dense Mamba decoder accuracy

Key Results

Metric	Performance
Complexity	O(k), where k = active detection events
Accuracy	Up to 49% MWPM logical error rate reduction at d ≤ 5 (SI1000)
Speed vs Tesseract	95-467× faster
Speed vs Belief Matching	232-463× faster
Latency	24-57 μs nearly constant across d = 3-9 (circuit-level noise)
Parameters	7.5M-16M parameters
Hardware	Commodity NVIDIA GPUs, no specialized accelerators

Benchmarks

• Depolarizing noise
• Uniform circuit-level noise
• SI1000 (Sycamore-inspired noise model)
• Google Sycamore experimental dataset

When to Use

• You need real-time or near-real-time QEC decoding at scale
• You want a neural decoder that scales to large code distances
• You need low-latency decoding for feedback in QEC cycles
• You're working with surface codes and want to leverage syndrome sparsity
• You want to explore Mamba/SSM architectures for physics tasks

Implementation Considerations

• Requires NVIDIA GPU for inference
• Implemented in PyTorch with 7.5M-16M parameters
• Mamba backbone can use the official Mamba implementation or custom SSM
• Defect encoding is critical: 13D feature vector encodes spatial + temporal + neighborhood info
• Ensemble decoding improves accuracy but increases compute proportionally

Comparison with Other Decoders

Decoder	Type	Complexity	Latency
SMD (this work)	Neural (Mamba)	O(k)	24-57 μs
MWPM	Classical	O(n³)	High
Tesseract	Near-MLD	High	95-467× slower
Belief Matching	Classical BP	O(n²)	232-463× slower
Dense Neural	Neural (CNN/Transformer)	O(d²R)	Moderate

Activation

Keywords: Sparse Mamba Decoder, SMD, quantum error correction, surface code, defect-centric decoding, state-space model, Mamba, QEC neural decoder, syndrome sparsity, real-time QEC, fault-tolerant quantum computing

References

• arXiv:2605.17156 — SMD original paper
• arXiv:2406.11082 — Mamba: Linear-Time Sequence Modeling with Selective State Spaces
• arXiv:2403.07888 — Dense Mamba decoder for QEC (Varbanov et al.)
• arXiv:2303.07205 — Surface code MWPM decoding
• arXiv:2207.06454 — Tensor network decoders
• arXiv:2406.03460 — Tesseract near-MLD decoder