neural-decoder-confidence-qec

name	neural-decoder-confidence-qec
description	Graph neural network decoder confidence as learned proxy for logical gap in quantum error correction. The logit of a pretrained GNN decoder acts as a reliable proxy for minimum-weight perfect matching (MWPM) logical gap, enabling soft-information error correction without the computational overhead. Use when designing QEC decoders, implementing soft-decision quantum error correction, or evaluating decoder reliability.
license	Complete terms in LICENSE.txt
metadata	{"arxiv_id":"2606.08758","published":"2026-06-07","authors":"David Dentelski","tags":["quantum-error-correction","GNN-decoder","logical-gap","MWPM"]}
allowed-tools	exec, read, write

Neural Decoder Confidence as Logical Gap Proxy

Description

Methodology from arXiv:2606.08758 (June 2026). Tests whether the logit of a graph neural network (GNN) decoder can act as a learned proxy for the logical gap in quantum error correction decoding.

Core Methodology

Problem

QEC decoders must infer the logical sector from measured syndrome. Beyond hard decisions, soft information estimating reliability is valuable. For MWPM, the logical gap (complementary gap) is a common confidence measure but computationally expensive.

Solution

Use the logit output of a pretrained GNN decoder as a learned proxy for the logical gap:

1. Train GNN decoder on surface code syndrome data for hard logical decisions
2. Extract logit values from the GNN output layer
3. Compare logit distribution against MWPM logical gap
4. Calibrate reliability — logits correlate with logical gap magnitude

Key Findings

• Pretrained GNN logits correlate strongly with MWPM logical gap
• GNN-based soft information is orders of magnitude faster to compute
• Enables real-time soft-decision decoding on quantum hardware
• Maintains decoding accuracy while providing confidence estimates

Implementation Patterns

Pattern 1: GNN Decoder with Confidence Output

import torch
import torch.nn as nn

class GNNQECDecoder(nn.Module):
    def __init__(self, hidden_dim=64):
        super().__init__()
        self.message_pass = GNNLayer(hidden_dim)
        self.readout = nn.Linear(hidden_dim, 1)
    
    def forward(self, syndrome_graph):
        # Message passing over syndrome graph
        node_features = self.message_pass(syndrome_graph)
        # Global pooling
        graph_repr = torch.mean(node_features, dim=0)
        # Logit output (proxy for logical gap)
        logit = self.readout(graph_repr).squeeze()
        return logit
    
    def decode(self, syndrome_graph):
        """Return hard decision + confidence."""
        logit = self.forward(syndrome_graph)
        prediction = torch.sign(logit)
        confidence = torch.sigmoid(torch.abs(logit))
        return prediction, confidence

Pattern 2: Calibration Against MWPM

def calibrate_gnn_confidence(gnn_model, mwpm_decoder, dataset):
    """Calibrate GNN logits against MWPM logical gap."""
    logits = []
    gaps = []
    
    for syndrome in dataset:
        logit = gnn_model(syndrome).item()
        gap = mwpm_decoder.logical_gap(syndrome)
        logits.append(logit)
        gaps.append(gap)
    
    # Fit calibration: |logit| ~ logical_gap
    correlation = np.corrcoef(np.abs(logits), gaps)[0, 1]
    return correlation

Pattern 3: Soft-Decision QEC Pipeline

class SoftQECDecoder:
    def __init__(self, gnn_model, threshold=0.5):
        self.model = gnn_model
        self.threshold = threshold
    
    def decode_with_confidence(self, syndrome):
        """Decode syndrome with reliability estimate."""
        prediction, confidence = self.model.decode(syndrome)
        
        if confidence < self.threshold:
            # Low confidence: flag for additional verification
            return {
                'decision': prediction,
                'confidence': confidence,
                'flagged': True
            }
        
        return {
            'decision': prediction,
            'confidence': confidence,
            'flagged': False
        }

When to Use

• Quantum error correction decoder design
• Real-time soft-decision decoding
• QEC systems requiring confidence estimates
• Replacing MWPM logical gap computation
• Neural QEC decoder development

Pitfalls

1. Logit scale differs from gap: GNN logits are not directly in gap units — calibration needed
2. Model generalization: GNN trained on one code distance may not transfer to others
3. Syndrome graph construction: Graph topology must match the underlying QEC code

References

• arXiv:2606.08758
• Related: dart-q-realtime-qldpc-decoding — real-time QLDPC decoding
• Related: sparse-mamba-qec-decoder — sparse Mamba QEC decoder