sparse-mamba-qec-decoder

name	sparse-mamba-qec-decoder
description	Sparse Mamba Decoder (SMD) for quantum error correction — defect-centric neural decoder using state-space (Mamba) backbone. Processes only k active detection events (O(k) complexity) instead of full O(d²R) syndrome array. Reduces MWPM logical error rate by up to 49%, runs 95-467x faster than Tesseract near-MLD, achieves 24-57μs latency across d=3-9. Activation: sparse mamba decoder, SMD, QEC neural decoder, surface code Mamba, defect-centric decoding, sparse syndrome processing, quantum error correction state space model.
category	quantum

Sparse Mamba Decoder for Quantum Error Correction

Defect-centric neural decoder for surface code syndromes using a Mamba (state-space model) backbone. Based on arXiv:2605.17156.

Problem Statement

Quantum error correction (QEC) requires decoders that are simultaneously accurate, fast, and scalable.

Existing limitation: State-of-the-art neural decoders process the full dense syndrome array of size O(d²R) regardless of actual error rate. At physically relevant error rates (p ~ 0.1%), fewer than 5% of syndrome entries contain active detection events — yet all existing decoders process the entire syndrome volume.

Core Innovation: Defect-Centric Sparse Processing

The Sparse Mamba Decoder (SMD) processes only the k active detection events using:

1. 13-dimensional feature representation per defect — compact encoding of each detection event's spatiotemporal properties
2. Mamba state-space backbone — linear-complexity sequence modeling of the defect stream
3. O(k) total complexity — decouples from code distance d and number of measurement rounds R

Feature Representation (13 dimensions per defect)

Each active detection event is encoded as a 13-dimensional vector capturing:

• Spatial coordinates (x, y position on the lattice)
• Temporal coordinate (measurement round)
• Syndrome type (X/Z basis indicators)
• Neighborhood context features
• Relative timing features

Architecture

Input: Raw syndrome array (d × d × R)
  ↓
Detection Event Extraction (sparse)
  ↓  k active detection events
13-dim Feature Embedding (per defect)
  ↓
Mamba State-Space Backbone (linear complexity)
  ↓
Output: Correction prediction

Results

Metric	Performance
Logical error rate vs MWPM (d ≤ 5, SI1000)	Up to 49% reduction
Speed vs Tesseract near-MLD	95-467× faster
Speed vs Belief Matching	232-463× faster
Latency (d = 3-9, uniform circuit-level noise)	Nearly constant 24-57 μs
Parameters	7.5-16M (commodity NVIDIA GPU)
Sycamore experimental dataset	Ensemble matches/surpasses dense Mamba decoder

When to Use

• Real-time surface code decoding on quantum hardware
• Low-latency QEC for fault-tolerant quantum computing
• Scalable neural decoders with sparse syndrome input
• Paring QEC decoding complexity with physical error rates
• FPGA/ASIC implementation of neural decoders

Design Principles

1. Exploit Sparsity at Source

At physically relevant error rates (p ~ 0.1%), <5% of syndrome entries are active. Processing only k active events yields O(k) complexity — a fundamental improvement over O(d²R). The sparsity is exponential at low error rates.

2. State-Space Models Over Transformers

Mamba's linear-complexity sequence modeling is ideal for the variable-length defect stream (k varies with error rate), avoiding the quadratic cost of self-attention.

3. Defect-Centric Over Dense

Unlike dense neural decoders that "see" the entire lattice, defect-centric processing focuses computation where errors actually occurred, dramatically reducing FLOPs.

4. Ensemble for Robustness

SMD ensemble matches or surpasses dense baselines, demonstrating that defect-centric processing does not sacrifice accuracy.

Implementation Considerations

Input Representation

• Extract detection events from syndrome using threshold-based or graph-based triggers
• 13-dim embedding: position (2), time (1), basis (1), neighborhood stats (4), relative timings (3), confidence (2)

Backbone

• Mamba block: selective scan with state dimension 16-64
• 4-8 Mamba layers stacked with residual connections
• Optional: cross-attention between defects for long-range interactions

Training

• Supervised on simulated noise data (depolarizing, circuit-level, Google Sycamore benchmarks)
• Loss: cross-entropy on correction prediction (or reinforcement learning for end-to-end)
• Data augmentation: rotate/translate lattice, vary error rate

Hardware Targets

• Commodity NVIDIA GPU for training
• Real-time inference on FPGA/ASIC for quantum hardware integration (sub-μs latency target)

Limitations

• Performance depends on accurate detection event extraction
• Very high error rates (p > 1%) reduce sparsity benefit
• Currently evaluated on surface codes only — generalization to other QEC codes is future work
• Training requires large simulated dataset at various noise rates

Related Work

• Tensor Network Decoders: Achieve high accuracy but scale poorly
• Transformer Decoders: High accuracy, O(L²) attention cost
• Dense Mamba Decoder (Varbanov et al.): First Mamba application to QEC but processes full syndrome
• Belief Matching: Fastest existing decoder at time of publication
• Tesseract near-MLD: High accuracy but very slow

Activation

sparse mamba decoder, SMD, QEC neural decoder, surface code Mamba, defect-centric decoding, sparse syndrome processing, quantum error correction state space model, Mamba QEC, neural QEC decoder, surface code decoder