Benchmarking Encoding Families in Quantum Neural Networks Under Fixed Circuit Area for Frequency Spectrum and Trainability

TL;DR

This paper systematically benchmarks various quantum neural network architectures and encoding strategies, analyzing their expressivity and trainability on synthetic and real-world datasets to guide optimal design choices.

Contribution

It provides new insights into how circuit architecture and frequency spectrum influence QNN trainability and expressivity, with practical guidelines for design.

Findings

Broader frequency spectra can enhance expressivity but may reduce trainability.

QNN performance improves with tailored frequency spectra matching task complexity.

More qubits and fewer layers generally improve trainability, except in single-layer architectures.

Abstract

Quantum Neural Networks (QNNs) offer a promising framework for integrating quantum computing principles into machine learning, yet their practical capabilities and limitations remain insufficiently studied. In this work, we systematically investigate the trainability and approximation properties of QNNs by benchmarking diverse circuit architectures and encoding strategies across synthetic and real-world datasets. We analyze several ans\"atze, including Hamming, binary, exponential, ternary, turnpike and Golomb, by evaluating their ability to learn synthetic data modeled as random finite Fourier series. To assess real-world applicability, we further evaluate QNNs on two time-series classification tasks: a Fischertechnik pneumatic leak detection dataset and the publicly available NASA bearing fault dataset. Our experiments show that while broader frequency spectra can theoretically enhance expressivity, practical trainability is strongly influenced by architectural factors such as qubit count and circuit depth. Notably, we find that QNNs perform best when the frequency spectrum is tailored to the target function's complexity but remains as compact as possible. Moreover, architectures with identical frequency spectra can differ in trainability, with configurations using more qubits and fewer layers generally performing better, except in the single-layer case. These findings provide guidelines for selecting QNN ans\"atze and offer new insights into the interplay between expressivity and trainability in quantum machine learning.