# A Survey of Quantum Learning Theory

arXiv: https://arxiv.org/abs/1701.06806 · HTML: https://mlsanity.com/paper/1701.06806/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2017.

## Built on by (most cited first, 12 of 12)

- [On the average-case complexity of learning output distributions of quantum circuits](https://mlsanity.com/paper/2305.05765/) (2023)
- [Quantum Vision Transformers for Quark-Gluon Classification](https://mlsanity.com/paper/2405.10284/) (2024)
- [Optimal quantum dataset for learning a unitary transformation](https://mlsanity.com/paper/2203.00546/) (2022)
- [Inference, interference and invariance: How the Quantum Fourier Transform can help to learn from data](https://mlsanity.com/paper/2409.00172/) (2024)
- [Generative Invertible Quantum Neural Networks](https://mlsanity.com/paper/2302.12906/) (2023)
- [Quantum Semi-Supervised Kernel Learning](https://mlsanity.com/paper/2204.10700/) (2022)
- [Fat Shattering, Joint Measurability, and PAC Learnability of POVM Hypothesis Classes](https://mlsanity.com/paper/2308.12304/) (2023)
- [Quantum Reinforcement Learning in Non-Abelian Environments: Unveiling Novel Formulations and Quantum Advantage Exploration](https://mlsanity.com/paper/2406.06531/) (2024)
- [New Bounds on Quantum Sample Complexity of Measurement Classes](https://mlsanity.com/paper/2408.12683/) (2024)
- [Lie-Equivariant Quantum Graph Neural Networks](https://mlsanity.com/paper/2411.15315/) (2024)
- [Hybrid Quantum-Classical Selective State Space Artificial Intelligence](https://mlsanity.com/paper/2511.08349/) (2025)
- [Advantage of Entangled Learning Rules in Quantum Measurement Class Learning](https://mlsanity.com/paper/2610.07328/) (2026)

## Abstract (arXiv)

This paper surveys quantum learning theory: the theoretical aspects of machine learning using quantum computers. We describe the main results known for three models of learning: exact learning from membership queries, and Probably Approximately Correct (PAC) and agnostic learning from classical or quantum examples.