# Hierarchical quantum circuit representations for neural architecture search

arXiv: https://arxiv.org/abs/2210.15073 · HTML: https://mlsanity.com/paper/2210.15073/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 54 references that are in the map.
- First posted on arXiv 26 Oct 2022.

## Builds on (most cited first, 9 of 9)

- [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)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Why does deep and cheap learning work so well?](https://mlsanity.com/paper/1608.08225/) (2016)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [Exploiting symmetry in variational quantum machine learning](https://mlsanity.com/paper/2205.06217/) (2022)
- [A Domain-agnostic, Noise-resistant, Hardware-efficient Evolutionary Variational Quantum Eigensolver](https://mlsanity.com/paper/1910.09694/) (2019)

## Built on by (most cited first, 9 of 9)

- [Quantum Circuit Design using a Progressive Widening Enhanced Monte Carlo Tree Search](https://mlsanity.com/paper/2502.03962/) (2025)
- [Optimizing Quantum Convolutional Neural Network Architectures for Arbitrary Data Dimension](https://mlsanity.com/paper/2403.19099/) (2024)
- [Quantum Circuit Training with Growth-Based Architectures](https://mlsanity.com/paper/2411.16560/) (2024)
- [Quantum Powered Credit Risk Assessment: A Novel Approach using hybrid Quantum-Classical Deep Neural Network for Row-Type Dependent Predictive Analysis](https://mlsanity.com/paper/2502.07806/) (2025)
- [HQCC: A Hybrid Quantum-Classical Classifier with Adaptive Structure](https://mlsanity.com/paper/2504.02167/) (2025)
- [Q-PhotoNAS: Hybrid Quantum Neural Architecture Search Framework on Photonic Devices](https://mlsanity.com/paper/2605.22097/) (2026)
- [Supervised Quantum Machine Learning: A Future Outlook from Qubits to Enterprise Applications](https://mlsanity.com/paper/2505.24765/) (2025)
- [Magic-Informed Quantum Architecture Search](https://mlsanity.com/paper/2605.03932/) (2026)
- [Evolving Hybrid Quantum-Classical Architectures for Image Classification](https://mlsanity.com/paper/2610.03220/) (2026)

## Abstract (arXiv)

Machine learning with hierarchical quantum circuits, usually referred to as Quantum Convolutional Neural Networks (QCNNs), is a promising prospect for near-term quantum computing. The QCNN is a circuit model inspired by the architecture of Convolutional Neural Networks (CNNs). CNNs are successful because they do not need manual feature design and can learn high-level features from raw data. Neural Architecture Search (NAS) builds on this success by learning network architecture and achieves state-of-the-art performance. However, applying NAS to QCNNs presents unique challenges due to the lack of a well-defined search space. In this work, we propose a novel framework for representing QCNN architectures using techniques from NAS, which enables search space design and architecture search. Using this framework, we generate a family of popular QCNNs, those resembling reverse binary trees. We then evaluate this family of models on a music genre classification dataset, GTZAN, to justify the importance of circuit architecture. Furthermore, we employ a genetic algorithm to perform Quantum Phase Recognition (QPR) as an example of architecture search with our representation. This work provides a way to improve model performance without increasing complexity and to jump around the cost landscape to avoid barren plateaus. Finally, we implement the framework as an open-source Python package to enable dynamic QCNN creation and facilitate QCNN search space design for NAS.