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

2026/03/25 by Vasilis Belis, Joseph Bowles, Rishabh Gupta +2 · 1 voice
Computer Science · Mathematics · Physics and Astronomy · #Fourier transform #Open quantum system #Quantum #Quantum Computing Algorithms and Architecture #Quantum Fourier transform #Quantum Mechanics and Applications #Quantum algorithm #Quantum computer #Quantum machine learning #Quantum many-body systems #Quantum state #cs.LG #quant-ph #stat.ML

paper · pdf · doi:10.48550/arxiv.2603.24654

openalex publication_date 2026/03/25 · arxiv published 2026/03/25 · openalex created_date 2026/03/28 · arxiv updated 2026/04/14 · openalex updated_date 2026/07/28

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 discuss this potential in detail here, hoping to stimulate a direction in quantum machine learning research that puts the question of ``why quantum?'' first.

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Discussions

• Haha fair enough 😅 genuine question: you're not so enthusiastic about some of the recent work on spectral methods (e.g. arxiv.org/abs/2603.24654), QELM/QRC (e.g. arxiv.org/abs/2603.13005) or hybrid Q [bsky, 0 points, 0 comments]

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