sparse-mamba-decoder-qec - SKILL.md Agent Skill

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