Neural Fourier Surrogates for Data Reuploading Quantum Neural Networks

2026-09-30

AI Summary

This study addresses the blurred boundary between quantum neural networks (QNNs) and classical models, which stems from the absence of fair comparison benchmarks. We propose the Neural Fourier Surrogate (NFS) architecture, which integrates neural quantum states with random Fourier feature techniques to efficiently learn coefficients under a unified Fourier basis. This approach constructs a classical surrogate network supporting finite Fourier series, serving as a natural classical baseline for evaluating data-reuploading QNNs. Experimental results demonstrate that NFS achieves performance comparable to both classical models and QNNs on tabular benchmarks. Consequently, this work establishes a rigorous and effective evaluation framework for quantifying potential quantum advantages in machine learning tasks.

Abstract

For quantum machine learning, the exact boundary between classical and quantum advantage is still poorly understood. Direct comparison between quantum neural networks (QNNs) and existing classical models, which encompass fundamentally different function classes, often fails to provide broader insight into the difference between the two. Inspired by the techniques of Neural Quantum States and Random Fourier Features, this work introduces Neural Fourier Surrogates (NFS), a stochastic classical neural network architecture for efficiently learning coefficients over the same finite Fourier series support as quantum neural networks. Testing on a selection of tabular benchmark datasets, we find that NFS is an effective classifier architecture broadly competitive with established classical baselines, including a comparable Random Fourier Features model, and possessing comparable performance to data-reuploading QNNs; combined with additional analysis comparing the learned Fourier spectra of QNNs and NFS on synthetic data, these results establish NFS as a natural classical baseline for evaluating QNN performance.

Problem

• Quantum Machine Learning
• Quantum Neural Networks
• Classical-Quantum Advantage
• Data Reuploading
• Fourier Series

Innovation

• Neural Fourier Surrogates
• Quantum Neural Networks
• Random Fourier Features
• Data Reuploading
• Classical Baseline