Hyperparameter Importance of Quantum Neural Networks Across Small Datasets
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.