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Deep Quantum Error Correction
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Proposes Quantum Error Correction Code Transformer (QECCT), an end-to-end transformer decoder that predicts an initial noise estimate from the syndrome, is optimized with a differentiable logical-error-rate loss, and pools over repeated noisy syndrome measurements.
Problem
Neural decoding of quantum error correction codes is hard because syndrome-only access (measurement collapse), the non-differentiable GF(2) logical error metric, and faulty syndrome measurements prevent direct application of classical ECC decoders; existing neural quantum decoders are computationall
Approach
Replace the channel magnitude input of the classical ECCT with a learned initial noise estimate computed from the syndrome, optimize the GF(2) logical error rate via a differentiable XOR-as-product mapping with sigmoid binarization, and handle noisy syndromes by time-averaging embeddings at the middle Transformer layer.</したcore_idea>
Key results
- On Toric codes with depolarization noise, QECCT reaches a threshold of 0.178 versus 0.157 for MWPM and 0.189 for ML.
- QECCT outperforms MWPM on independent-noise Toric codes with and without noisy syndrome measurements.
- QECCT also outperforms MWPM on Surface codes under depolarization and circuit noise.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use QECCT instead of MWPM | Toric code decoding · Depolarization noise | threshold: 0.157 -> 0.178 | Helped |
| Train with the BER objective only instead of combined objectives (ablation) | QECCT · High SNR | LER: 27 times higher LER | Hurt |
| Add the noise-estimator objective L_g (ablation) | QECCT · High SNR | LER: 46% improvement | Helped |
| Pool at the middle network layer instead of the initial embedding (ablation) | QECCT with repeated syndrome measurements · Toric code | LER: 5% lower | Helped |
| Replace learned noise estimator g_ω with constant mapping g_ω = 1_n (ablation) | QECCT · Toric code | LER | Hurt |
| Use a one-hidden-layer or three-hidden-layer noise estimator (ablation) | QECCT · Toric code | LER | No clear effect |
| Train using the LER objective alone (ablation) | QECCT · Toric code | LER | Hurt |
| Add the LER objective to BER-only training (ablation) | QECCT · High SNR | LER: 27 times higher LER | Helped |
| Pool at the final embedding instead of the middle layer (ablation) | QECCT with repeated syndrome measurements · Toric code | decoding performance | Hurt |
| Remove the parity-check-derived attention mask (ablation) | QECCT · Toric code | accuracy | Hurt |
| Increase network capacity (ablation) | QECCT · Toric code | accuracy | Helped |
| Use the straight-through estimator instead of sigmoid as the binarization function (ablation) | QECCT · Toric code | performance | Hurt |
Surprising findings
- Training solely with the logical error rate loss converges quickly to a bad local minimum.
- A BER-only trained model yields 27 times higher LER than the combined-objective model at high SNR.
Limitations
- Straightforward implementation is hard to scale to larger codes or more syndrome repetitions due to unstructured sparse attention.
- Performance slightly lower threshold at L=10 with depolarization noise, suggesting tuning of regularization weights is needed.
- Larger architectures and longer training were not tested due to limited compute.
Experimental setup
Datasets: simulated toric code noise simulated surface code noise STIM circuit noise simulations
Benchmarks: Toric codes (independent and depolarization noise) Surface codes (depolarization and circuit noise)
Metrics: logical error rate bit error rate threshold
Baselines: MWPM Union-Find ML decoder (threshold reference) MLP decoder
Builds on: ECCT Transformer minimum-weight perfect matching
Closest papers by meaning
- QEM-Bench: Benchmarking Learning-based Quantum Error Mitigation and QEMFormer as a Multi-ranged Context Learning Baseline (ICML 2025 · similarity 0.83)
- ATP: Adaptive Threshold Pruning for Efficient Data Encoding in Quantum Neural Networks (CVPR 2025 · similarity 0.83)
- Quantum Deep Equilibrium Models (NeurIPS 2024 · similarity 0.82)
- Toward the Goldilocks Blind Compression of Quantum States (NeurIPS 2026 · similarity 0.82)
- Qsco: A Quantum Scoring Module for Open-Set Supervised Anomaly Detection (AAAI 2025 · similarity 0.82)
- Non-asymptotic Approximation Error Bounds of Parameterized Quantum Circuits (NeurIPS 2024 · similarity 0.81)
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