Quantum Random Features: A Spectral Framework for Quantum Machine Learning
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918313383165952 |
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| author | Sakurai, Akitada Hayashi, Aoi Munro, William John Nemoto, Kae |
| author_facet | Sakurai, Akitada Hayashi, Aoi Munro, William John Nemoto, Kae |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21746 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Random Features: A Spectral Framework for Quantum Machine Learning Sakurai, Akitada Hayashi, Aoi Munro, William John Nemoto, Kae Quantum Physics 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. |
| title | Quantum Random Features: A Spectral Framework for Quantum Machine Learning |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.21746 |