# Learning Encodings by Maximizing State Distinguishability: Variational Quantum Error Correction

arXiv: https://arxiv.org/abs/2506.11552 · HTML: https://mlsanity.com/paper/2506.11552/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 129 references that are in the map.
- First posted on arXiv 13 Jun 2025.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Stability of Stochastic Gradient Descent on Nonsmooth Convex Losses](https://mlsanity.com/paper/2006.06914/) (2020)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [A Survey on Quantum Reinforcement Learning](https://mlsanity.com/paper/2211.03464/) (2022)
- [Learning to Decode the Surface Code with a Recurrent, Transformer-Based Neural Network](https://mlsanity.com/paper/2310.05900/) (2023)
- [Challenges and Opportunities in Quantum Optimization](https://mlsanity.com/paper/2312.02279/) (2023)
- [Optimizing Quantum Error Correction Codes with Reinforcement Learning](https://mlsanity.com/paper/1812.08451/) (2018)
- [Automated Quantum Circuit Design with Nested Monte Carlo Tree Search](https://mlsanity.com/paper/2207.00132/) (2022)
- [Variational Quantum Algorithms for Trace Distance and Fidelity Estimation](https://mlsanity.com/paper/2012.05768/) (2020)
- [Benchmarking Quantum Reinforcement Learning](https://mlsanity.com/paper/2501.15893/) (2025)
- [Qiskit-Torch-Module: Fast Prototyping of Quantum Neural Networks](https://mlsanity.com/paper/2404.06314/) (2024)
- [Quantum Codes from Neural Networks](https://mlsanity.com/paper/1806.08781/) (2018)
- [Discovery of Optimal Quantum Error Correcting Codes via Reinforcement Learning](https://mlsanity.com/paper/2305.06378/) (2023)
- [Discovering highly efficient low-weight quantum error-correcting codes with reinforcement learning](https://mlsanity.com/paper/2502.14372/) (2025)
- [Warm-Start Variational Quantum Policy Iteration](https://mlsanity.com/paper/2404.10546/) (2024)
- [Quantum Autoencoders for Learning Quantum Channel Codes](https://mlsanity.com/paper/2307.06622/) (2023)
- [Enhancing Quantum Memory Lifetime with Measurement-Free Local Error Correction and Reinforcement Learning](https://mlsanity.com/paper/2408.09524/) (2024)

## Built on by (most cited first, 1 of 1)

- [Learning Logical Operations for Arbitrary Quantum Error Correction Codes](https://mlsanity.com/paper/2605.28162/) (2026)

## Abstract (arXiv)

Quantum error correction is crucial for protecting quantum information against decoherence. Traditional codes like the surface code require substantial overhead, making them impractical for near-term, early fault-tolerant devices. We propose a novel objective function for tailoring error correction codes to specific noise structures by maximizing the distinguishability between quantum states after a noise channel, ensuring efficient recovery operations. We formalize this concept with the distinguishability loss function, serving as a machine learning objective to discover resource-efficient encoding circuits optimized for given noise characteristics. We implement this methodology using variational techniques, termed variational quantum error correction (VarQEC). Our approach yields codes with desirable theoretical and practical properties and outperforms standard codes in various scenarios. We also provide proof-of-concept demonstrations on IBM and IQM hardware devices, highlighting the practical relevance of our procedure.