# Hyperparameter Importance of Quantum Neural Networks Across Small Datasets

arXiv: https://arxiv.org/abs/2206.09992 · HTML: https://mlsanity.com/paper/2206.09992/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 50 references that are in the map.
- First posted on arXiv 20 Jun 2022.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [OpenML Benchmarking Suites](https://mlsanity.com/paper/1708.03731/) (2017)
- [Auto-Sklearn 2.0: Hands-free AutoML via Meta-Learning](https://mlsanity.com/paper/2007.04074/) (2020)
- [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018)
- [Quantum machine learning beyond kernel methods](https://mlsanity.com/paper/2110.13162/) (2021)
- [Parametrized quantum policies for reinforcement learning](https://mlsanity.com/paper/2103.05577/) (2021)
- [Encoding-dependent generalization bounds for parametrized quantum circuits](https://mlsanity.com/paper/2106.03880/) (2021)
- [Hyperparameter Importance Across Datasets](https://mlsanity.com/paper/1710.04725/) (2017)
- [On the Quantum versus Classical Learnability of Discrete Distributions](https://mlsanity.com/paper/2007.14451/) (2020)
- [QuantumNAT: Quantum Noise-Aware Training with Noise Injection, Quantization and Normalization](https://mlsanity.com/paper/2110.11331/) (2021)
- [Learning Curves for Decision Making in Supervised Machine Learning: A Survey](https://mlsanity.com/paper/2201.12150/) (2022)
- [QOC: Quantum On-Chip Training with Parameter Shift and Gradient Pruning](https://mlsanity.com/paper/2202.13239/) (2022)
- [High Dimensional Quantum Machine Learning With Small Quantum Computers](https://mlsanity.com/paper/2203.13739/) (2022)
- [Quantum Machine Learning Framework for Virtual Screening in Drug Discovery: a Prospective Quantum Advantage](https://mlsanity.com/paper/2204.04017/) (2022)
- [Quantum Deep Reinforcement Learning for Robot Navigation Tasks](https://mlsanity.com/paper/2202.12180/) (2022)
- [Quantum Machine Learning For Classical Data](https://mlsanity.com/paper/2105.03684/) (2021)

## Built on by (most cited first, 7 of 7)

- [A Hyperparameter Study for Quantum Kernel Methods](https://mlsanity.com/paper/2310.11891/) (2023)
- [Application of quantum-inspired generative models to small molecular datasets](https://mlsanity.com/paper/2304.10867/) (2023)
- [FissionFusion: Fast Geometric Generation and Hierarchical Souping for Medical Image Analysis](https://mlsanity.com/paper/2403.13341/) (2024)
- [QuXAI: Explainers for Hybrid Quantum Machine Learning Models](https://mlsanity.com/paper/2505.10167/) (2025)
- [On Optimizing Hyperparameters for Quantum Neural Networks](https://mlsanity.com/paper/2403.18579/) (2024)
- [Quantum Re-Uploading for Calorimetry: Optimized Architectures with Extended Expressivity](https://mlsanity.com/paper/2412.12397/) (2024)
- [AQMLator -- An Auto Quantum Machine Learning E-Platform](https://mlsanity.com/paper/2409.18338/) (2024)

## Abstract (arXiv)

As restricted quantum computers are slowly becoming a reality, the search for meaningful first applications intensifies. In this domain, one of the more investigated approaches is the use of a special type of quantum circuit - a so-called quantum neural network -- to serve as a basis for a machine learning model. Roughly speaking, as the name suggests, a quantum neural network can play a similar role to a neural network. However, specifically for applications in machine learning contexts, very little is known about suitable circuit architectures, or model hyperparameters one should use to achieve good learning performance. In this work, we apply the functional ANOVA framework to quantum neural networks to analyze which of the hyperparameters were most influential for their predictive performance. We analyze one of the most typically used quantum neural network architectures. We then apply this to 7 open-source datasets from the OpenML-CC18 classification benchmark whose number of features is small enough to fit on quantum hardware with less than 20 qubits. Three main levels of importance were detected from the ranking of hyperparameters obtained with functional ANOVA. Our experiment both confirmed expected patterns and revealed new insights. For instance, setting well the learning rate is deemed the most critical hyperparameter in terms of marginal contribution on all datasets, whereas the particular choice of entangling gates used is considered the least important except on one dataset. This work introduces new methodologies to study quantum machine learning models and provides new insights toward quantum model selection.