[2603.24654] Spectral methods: crucial for machine learning, natural for quantum computers?

Quantum Physics arXiv:2603.24654 (quant-ph) [Submitted on 25 Mar 2026] Title:Spectral methods: crucial for machine learning, natural for quantum computers? Authors:Vasilis Belis, Joseph Bowles, Rishabh Gupta, Evan Peters, Maria Schuld View a PDF of the paper titled Spectral methods: crucial for machine learning, natural for quantum computers?, by Vasilis Belis and 4 other authors View PDF Abstract: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 discu...