Quantum Random Features: A Spectral Framework for Quantum Machine Learning

Quantum machine learning (QML) models often require deep, parameterized circuits to capture complex frequency components, limiting their scalability and near-term implementation. We introduce Quantum Random Features (QRF) and Quantum Dynamical Random Features (QDRF), lightweight quantum reservoir models inspired by classical random Fourier features (RFF) that generate high-dimensional spectral representations without variational optimization. Using Z-rotation encoding combined with random permutations or Hamiltonian dynamics, these models achieve N_f-dimensional feature maps at preprocessing cost O\(log(N_f\)). Spectral analysis shows that QRF and QDRF reproduce the behavior of RFF, while simulations on Fashion-MNIST reach up to 89.3% accuracy-matching or surpassing classical baselines with scalable qubit requirements. By linking spectral theory with experimentally feasible quantum dynamics, this work provides a compact and hardware-compatible route to scalable quantum learning.