# A scalable and real-time neural decoder for topological quantum codes

arXiv: https://arxiv.org/abs/2512.07737 · HTML: https://mlsanity.com/paper/2512.07737/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 57 references that are in the map.
- First posted on arXiv 8 Dec 2025.

## Builds on (most cited first, 11 of 11)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Symbolic Discovery of Optimization Algorithms](https://mlsanity.com/paper/2302.06675/) (2023)
- [Gated Attention for Large Language Models: Non-linearity, Sparsity, and Attention-Sink-Free](https://mlsanity.com/paper/2505.06708/) (2025)
- [Griffin: Mixing Gated Linear Recurrences with Local Attention for Efficient Language Models](https://mlsanity.com/paper/2402.19427/) (2024)
- [Learning to Decode the Surface Code with a Recurrent, Transformer-Based Neural Network](https://mlsanity.com/paper/2310.05900/) (2023)
- [Efficient and Universal Neural-Network Decoder for Stabilizer-Based Quantum Error Correction](https://mlsanity.com/paper/2502.19971/) (2025)
- [Minimum-Weight Parity Factor Decoder for Quantum Error Correction](https://mlsanity.com/paper/2508.04969/) (2025)

## Built on by (most cited first, 9 of 9)

- [Scalable Neural Decoders for Practical Fault-Tolerant Quantum Computation](https://mlsanity.com/paper/2604.08358/) (2026)
- [OmniQEC: discovering practical quantum error-correcting codes by an AI scientist](https://mlsanity.com/paper/2607.25865/) (2026)
- [Rethink the Role of Neural Decoders in Quantum Error Correction](https://mlsanity.com/paper/2605.12046/) (2026)
- [Learning to Decode in Parallel: Self-Coordinating Neural Network for Real-Time Quantum Error Correction](https://mlsanity.com/paper/2601.09921/) (2026)
- [Maximum Likelihood Decoding of Quantum Error Correction Codes](https://mlsanity.com/paper/2605.17230/) (2026)
- [Efficient foundation decoders for fault-tolerant quantum computing](https://mlsanity.com/paper/2606.27119/) (2026)
- [Machine Learning Approaches to Decoding Topological Quantum Codes](https://mlsanity.com/paper/2608.15760/) (2026)
- [Sparse Mamba Decoder for Quantum Error Correction: Efficient Defect-Centric Processing of Surface Code Syndromes](https://mlsanity.com/paper/2605.17156/) (2026)
- [Distance Prediction for Quantum Codes](https://mlsanity.com/paper/2610.18130/) (2026)

## Abstract (arXiv)

Fault-tolerant quantum computing will require error rates far below those achievable with physical qubits. Quantum error correction (QEC) bridges this gap, but depends on decoders being simultaneously fast, accurate, and scalable. This combination of requirements remains unmet by a machine-learning decoder, nor by any decoder for promising resource-efficient codes such as the color code. Here we introduce AlphaQubit 2, a neural-network decoder that achieves near-optimal logical error rates for both surface and color codes at scale under realistic noise. For the color code, it is orders of magnitude faster than other high-accuracy decoders. We demonstrate real-time decoding faster than 1μs per cycle on commercial accelerators: for the surface code to distance 11, with better accuracy than leading real-time decoders; and the first real-time decoding of the color code to distance 9. These results support the practical application of a wider class of promising QEC codes, and establish a credible path towards high-accuracy, real-time neural decoding at the scales required for fault-tolerant quantum computation.