Quantum Random Features: A Spectral Framework for Quantum Machine Learning

TL;DR

This paper introduces Quantum Random Features (QRF) and Quantum Dynamical Random Features (QDRF), lightweight quantum models inspired by classical spectral methods, enabling scalable quantum machine learning without deep circuits.

Contribution

It proposes novel quantum reservoir models that generate high-dimensional spectral features efficiently, bridging spectral theory with practical quantum dynamics for scalable learning.

Findings

Achieves up to 89.3% accuracy on Fashion-MNIST

Reproduces classical RFF spectral behavior in quantum models

Requires only logarithmic preprocessing cost

Abstract

Quantum machine learning (QML) models often require deep, parameterized circuits to capture complex frequency components, limiting their scalability and near-term implementation. We introduce \textit{Quantum Random Features} (QRF) and \textit{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.