Quantum Random Features: A Spectral Framework for Quantum Machine Learning

• URL: http://arxiv.org/abs/2601.21746v1
• Date: Thu, 29 Jan 2026 14:01:52 GMT
• Title: Quantum Random Features: A Spectral Framework for Quantum Machine Learning
• Authors: Akitada Sakurai, Aoi Hayashi, William John Munro, Kae Nemoto,
• Abstract summary: We introduce textitQuantum Random Features (QRF) and textitQuantum Dynamical Random Features (QDRF)<n>QRF and QDRF generate high-dimensional spectral representations without variational optimization.<n>By linking spectral theory with experimentally feasible quantum dynamics, this work provides a compact and hardware-compatible route to scalable quantum learning.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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