# Learning to Decode in Parallel: Self-Coordinating Neural Network for Real-Time Quantum Error Correction

arXiv: https://arxiv.org/abs/2601.09921 · HTML: https://mlsanity.com/paper/2601.09921/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 69 references that are in the map.
- First posted on arXiv 14 Jan 2026.

## Builds on (most cited first, 19 of 19)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Learning to Decode the Surface Code with a Recurrent, Transformer-Based Neural Network](https://mlsanity.com/paper/2310.05900/) (2023)
- [Goal-Aware Neural SAT Solver](https://mlsanity.com/paper/2106.07162/) (2021)
- [A scalable and real-time neural decoder for topological quantum codes](https://mlsanity.com/paper/2512.07737/) (2025)
- [Neural Network Decoders for Large-Distance 2D Toric Codes](https://mlsanity.com/paper/1809.06640/) (2018)
- [Efficient and Universal Neural-Network Decoder for Stabilizer-Based Quantum Error Correction](https://mlsanity.com/paper/2502.19971/) (2025)
- [Fusion Blossom: Fast MWPM Decoders for QEC](https://mlsanity.com/paper/2305.08307/) (2023)
- [A Scalable, Fast and Programmable Neural Decoder for Fault-Tolerant Quantum Computation Using Surface Codes](https://mlsanity.com/paper/2305.15767/) (2023)
- [A Classical Architecture For Digital Quantum Computers](https://mlsanity.com/paper/2305.14304/) (2023)
- [Micro Blossom: Accelerated Minimum-Weight Perfect Matching Decoding for Quantum Error Correction](https://mlsanity.com/paper/2502.14787/) (2025)

## Built on by (most cited first, 2 of 2)

- [Maximum Likelihood Decoding of Quantum Error Correction Codes](https://mlsanity.com/paper/2605.17230/) (2026)
- [Machine Learning Approaches to Decoding Topological Quantum Codes](https://mlsanity.com/paper/2608.15760/) (2026)

## Abstract (arXiv)

Fast, reliable decoders are pivotal components for enabling fault-tolerant quantum computation (FTQC). Neural network decoders like AlphaQubit have demonstrated potential, achieving higher accuracy than traditional human-designed decoding algorithms. However, existing implementations of neural network decoders lack the parallelism required to decode the syndrome stream generated by a superconducting logical qubit in real time. Moreover, integrating AlphaQubit with sliding window-based parallel decoding schemes presents non-trivial challenges: AlphaQubit is trained solely to output a single bit corresponding to the global logical correction for an entire memory experiment, rather than local physical corrections that can be easily integrated. We address this issue by training a recurrent, transformer-based neural network specifically tailored for parallel window decoding. While it still outputs a single bit, we derive training labels from a consistent set of local corrections and train on various types of decoding windows simultaneously. This approach enables the network to self-coordinate across neighboring windows, facilitating high-accuracy parallel decoding of arbitrarily long memory experiments. As a result, we overcome the throughput bottleneck that previously precluded the use of AlphaQubit-type decoders in FTQC. Our work presents the first scalable, neural-network-based parallel decoding framework that simultaneously achieves SOTA accuracy and the stringent throughput required for real-time quantum error correction. Using an end-to-end experimental workflow, we benchmark our decoder on the Zuchongzhi 3.2 superconducting quantum processor on surface codes with distances up to 7, demonstrating its superior accuracy. Moreover, we demonstrate that, using our approach, a single TPU v6e is capable of decoding surface codes with distances up to 25 within 1us per decoding round.