# Deep Quantum Error Correction

arXiv: https://arxiv.org/abs/2301.11930 · HTML: https://mlsanity.com/paper/2301.11930/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 71 references that are in the map.
- First posted on arXiv 27 Jan 2023.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [A Survey of Transformers](https://mlsanity.com/paper/2106.04554/) (2021)
- [Learning to Decode Linear Codes Using Deep Learning](https://mlsanity.com/paper/1607.04793/) (2016)
- [Error Correction Code Transformer](https://mlsanity.com/paper/2203.14966/) (2022)
- [Communication Algorithms via Deep Learning](https://mlsanity.com/paper/1805.09317/) (2018)
- [Hyper-Graph-Network Decoders for Block Codes](https://mlsanity.com/paper/1909.09036/) (2019)
- [Deep Learning for Decoding of Linear Codes - A Syndrome-Based Approach](https://mlsanity.com/paper/1802.04741/) (2018)
- [Reinforcement Learning Decoders for Fault-Tolerant Quantum Computation](https://mlsanity.com/paper/1810.07207/) (2018)
- [Neural Offset Min-Sum Decoding](https://mlsanity.com/paper/1701.05931/) (2017)
- [Denoising Diffusion Error Correction Codes](https://mlsanity.com/paper/2209.13533/) (2022)
- [Deep neural decoders for near term fault-tolerant experiments](https://mlsanity.com/paper/1802.06441/) (2018)

## Built on by (most cited first, 11 of 11)

- [Learning to Decode the Surface Code with a Recurrent, Transformer-Based Neural Network](https://mlsanity.com/paper/2310.05900/) (2023)
- [Learning Linear Block Error Correction Codes](https://mlsanity.com/paper/2405.04050/) (2024)
- [Hybrid Mamba-Transformer Decoder for Error-Correcting Codes](https://mlsanity.com/paper/2505.17834/) (2025)
- [Factor Graph Optimization of Error-Correcting Codes for Belief Propagation Decoding](https://mlsanity.com/paper/2406.12900/) (2024)
- [Accelerating Error Correction Code Transformers](https://mlsanity.com/paper/2410.05911/) (2024)
- [Toward Uncertainty-Aware and Generalizable Neural Decoding for Quantum LDPC Codes](https://mlsanity.com/paper/2510.06257/) (2025)
- [Neural Minimum Weight Perfect Matching for Quantum Error Codes](https://mlsanity.com/paper/2601.00242/) (2026)
- [Disturbance-based Discretization, Differentiable IDS Channel, and an IDS-Correcting Code for DNA-based Storage](https://mlsanity.com/paper/2407.18929/) (2024)
- [SAQ: Stabilizer-Aware Quantum Error Correction Decoder](https://mlsanity.com/paper/2512.08914/) (2025)
- [A Mixture of Experts Vision Transformer for High-Fidelity Surface Code Decoding](https://mlsanity.com/paper/2601.12483/) (2026)
- [When AI meets quantum information: A comprehensive review](https://mlsanity.com/paper/2607.00365/) (2026)

## Abstract (arXiv)

Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. QECC, as its classical counterpart (ECC), enables the reduction of error rates, by distributing quantum logical information across redundant physical qubits, such that errors can be detected and corrected. In this work, we efficiently train novel end-to-end deep quantum error decoders. We resolve the quantum measurement collapse by augmenting syndrome decoding to predict an initial estimate of the system noise, which is then refined iteratively through a deep neural network. The logical error rates calculated over finite fields are directly optimized via a differentiable objective, enabling efficient decoding under the constraints imposed by the code. Finally, our architecture is extended to support faulty syndrome measurement, by efficient decoding of repeated syndrome sampling. The proposed method demonstrates the power of neural decoders for QECC by achieving state-of-the-art accuracy, outperforming for small distance topological codes, the existing end-to-end neural and classical decoders, which are often computationally prohibitive.