Hyperparameter Importance of Quantum Neural Networks Across Small Datasets

TL;DR

This paper investigates the influence of hyperparameters on quantum neural network performance across small datasets, revealing key factors like learning rate and entangling gates through a novel analysis framework.

Contribution

It applies the functional ANOVA framework to analyze hyperparameter importance in quantum neural networks, providing new insights for model selection and methodology in quantum machine learning.

Findings

Learning rate is the most critical hyperparameter across datasets.

Choice of entangling gates is generally less important.

New methodology introduced for analyzing quantum model hyperparameters.

Abstract

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.