# Learning to Concatenate Quantum Codes

arXiv: https://arxiv.org/abs/2604.14931 · HTML: https://mlsanity.com/paper/2604.14931/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 37 references that are in the map.
- First posted on arXiv 16 Apr 2026.

## Builds on (most cited first, 3 of 3)

- [Optimizing Quantum Error Correction Codes with Reinforcement Learning](https://mlsanity.com/paper/1812.08451/) (2018)
- [Qiskit-Torch-Module: Fast Prototyping of Quantum Neural Networks](https://mlsanity.com/paper/2404.06314/) (2024)
- [Warm-Start Variational Quantum Policy Iteration](https://mlsanity.com/paper/2404.10546/) (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)

Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an optimal code sequence. We automate this choice by estimating the effective noise channel after each level and selecting the next code accordingly. In particular, we use learning-based methods to tailor small, non-additive encoders when the noise exhibits sufficient structure, then switch to standard codes once the noise is nearly uniform. In simulations, this level-wise adaptation achieves a target logical error rate with far fewer qubits than concatenating stabilizer codes alone--reducing qubit counts by up to two orders of magnitude for strongly structured noise. Therefore, this hybrid, learning-based strategy offers a promising tool for early fault-tolerant quantum computing.