# What can we learn from quantum convolutional neural networks?

arXiv: https://arxiv.org/abs/2308.16664 · HTML: https://mlsanity.com/paper/2308.16664/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 100 references that are in the map.
- First posted on arXiv 31 Aug 2023.

## Builds on (most cited first, 25 of 25)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Transfer learning in hybrid classical-quantum neural networks](https://mlsanity.com/paper/1912.08278/) (2019)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality](https://mlsanity.com/paper/2006.10593/) (2020)
- [Encoding-dependent generalization bounds for parametrized quantum circuits](https://mlsanity.com/paper/2106.03880/) (2021)
- [The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine](https://mlsanity.com/paper/1904.02214/) (2019)
- [Understanding quantum machine learning also requires rethinking generalization](https://mlsanity.com/paper/2306.13461/) (2023)
- [Active learning machine learns to create new quantum experiments](https://mlsanity.com/paper/1706.00868/) (2017)
- [Recent advances for quantum classifiers](https://mlsanity.com/paper/2108.13421/) (2021)
- [Entangled Datasets for Quantum Machine Learning](https://mlsanity.com/paper/2109.03400/) (2021)
- [Quantum Self-Supervised Learning](https://mlsanity.com/paper/2103.14653/) (2021)
- [Higgs analysis with quantum classifiers](https://mlsanity.com/paper/2104.07692/) (2021)
- [Foundations for learning from noisy quantum experiments](https://mlsanity.com/paper/2204.13691/) (2022)
- [Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Series](https://mlsanity.com/paper/2108.03190/) (2021)
- [Protocols for classically training quantum generative models on probability distributions](https://mlsanity.com/paper/2210.13442/) (2022)

## Built on by (most cited first, 6 of 6)

- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Partitioned Hybrid Quantum Fourier Neural Operators for Scientific Quantum Machine Learning](https://mlsanity.com/paper/2507.08746/) (2025)
- [Geometric quantum machine learning of BQPA protocols and latent graph classifiers](https://mlsanity.com/paper/2402.03871/) (2024)
- [Learnable quantum spectral filters for hybrid graph neural networks](https://mlsanity.com/paper/2507.05640/) (2025)
- [Permutation-equivariant quantum convolutional neural networks](https://mlsanity.com/paper/2404.18198/) (2024)
- [Can Geometric Quantum Machine Learning Lead to Advantage in Barcode Classification?](https://mlsanity.com/paper/2409.01496/) (2024)

## Abstract (arXiv)

Quantum machine learning (QML) shows promise for analyzing quantum data. A notable example is the use of quantum convolutional neural networks (QCNNs), implemented as specific types of quantum circuits, to recognize phases of matter. In this approach, ground states of many-body Hamiltonians are prepared to form a quantum dataset and classified in a supervised manner using only a few labeled examples. However, this type of dataset and model differs fundamentally from typical QML paradigms based on feature maps and parameterized circuits. In this study, we demonstrate how models utilizing quantum data can be interpreted through hidden feature maps, where physical features are implicitly embedded via ground-state feature maps. By analyzing selected examples previously explored with QCNNs, we show that high performance in quantum phase recognition comes from generating a highly effective basis set with sharp features at critical points. The learning process adapts the measurement to create sharp decision boundaries. Our analysis highlights improved generalization when working with quantum data, particularly in the limited-shots regime. Furthermore, translating these insights into the domain of quantum scientific machine learning, we demonstrate that ground-state feature maps can be applied to fluid dynamics problems, expressing shock wave solutions with good generalization and proven trainability.