Spectral methods: crucial for machine learning, natural for quantum computers?

Quantum Physics [Submitted on 25 Mar 2026] Spectral methods: crucial for machine learning, natural for quantum computers? Vasilis Belis, Joseph Bowles, Rishabh Gupta, Evan Peters, Maria Schuld This article presents an argument for why quantum computers could unlock new methods for machine learning. We argue that spectral methods, in particular those that learn, regularise, or otherwise manipulate the Fourier spectrum of a machine learning model, are often natural for quantum computers. For example, if a generative machine learning model is represented by a quantum state, the Quantum Fourier Transform allows us to manipulate the Fourier spectrum of the state using the entire toolbox of quantum routines, an operation that is usually prohibitive for classical models. At the same time, spectral methods are surprisingly fundamental to machine learning: A spectral bias has recently been hypothesised to be the core principle behind the success of deep learning; support vector machines have been known for decades to regularise in Fourier space, and convolutional neural nets build filters in the Fourier space of images. Could, then, quantum computing open fundamentally different, much more direct and resource-efficient ways to design the spectral properties of a model? We discuss this potential in detail here, hoping to stimulate a direction in quantum machine learning research that puts the question of ``why quantum?'' first. Comments: 25 pages, 8 figures Subjects: Quantum Physics (quant-ph); Machine Learning (cs.LG); Machine Learning (stat.ML) Cite as: arXiv:2603.24654 [quant-ph]   (or arXiv:2603.24654v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.24654 Focus to learn more Submission history From: Evan Peters [view email] [v1] Wed, 25 Mar 2026 18:00:00 UTC (515 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.LG stat stat.ML References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)