Spectral methods: crucial for machine learning, natural for quantum computers?
Not on the map. Why?
Abstract (arXiv)
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.
Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 44 of its 108 references that are in the map. First posted on arXiv 25 Mar 2026.
Builds on
44 of 108 references.
References · 44
- 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
- 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,597
- 2018The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networkscited by 2,250
- 2016Understanding deep learning requires rethinking generalizationcited by 1,657
- 2018Spectral Normalization for Generative Adversarial Networkscited by 1,618
- 2016On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minimacited by 1,337
- 2018On the Spectral Bias of Neural Networkscited by 1,321
- 2018Reconciling modern machine learning practice and the bias-variance trade-offcited by 919
- 2019On Exact Computation with an Infinitely Wide Neural Netcited by 572
- 2019Benign Overfitting in Linear Regressioncited by 544
- 2015Deep Kernel Learningcited by 440
32 more
- 2019Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networkscited by 360
- 2021FNet: Mixing Tokens with Fourier Transformscited by 343
- 2020The effect of data encoding on the expressive power of variational quantum machine learning modelscited by 328
- 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
- 2017MMD GAN: Towards Deeper Understanding of Moment Matching Networkcited by 251
- 2019SGD on Neural Networks Learns Functions of Increasing Complexitycited by 203
- 2023Challenges and Opportunities in Quantum Machine Learningcited by 202
- 2021Quantum advantage in learning from experimentscited by 186
- 2019Towards Understanding the Spectral Bias of Deep Learningcited by 173
- 2020The Hardware Lotterycited by 160
- 2020Frequency Bias in Neural Networks for Input of Non-Uniform Densitycited by 140
- 2013Gaussian Process Kernels for Pattern Discovery and Extrapolationcited by 131
- 2024Barren Plateaus in Variational Quantum Computingcited by 130
- 2016Learning in Implicit Generative Modelscited by 124
- 2018Differentiable Learning of Quantum Circuit Born Machinecited by 90
- 2024Better than classical? The subtle art of benchmarking quantum machine learning modelscited by 82
- 2021The Promises and Pitfalls of Deep Kernel Learningcited by 81
- 2023Does provable absence of barren plateaus imply classical simulability?cited by 78
- 2017Regularizing Deep Neural Networks by Noise: Its Interpretation and Optimizationcited by 56
- 2020A case for new neural network smoothness constraintscited by 43
- 2022Classical surrogates for quantum learning modelscited by 39
- 2022Why neural networks find simple solutions: the many regularizers of geometric complexitycited by 38
- 2023Trainability barriers and opportunities in quantum generative modelingcited by 35
- 2019Benchmarking the Neural Linear Model for Regressioncited by 31
- 2023Let Quantum Neural Networks Choose Their Own Frequenciescited by 22
- 2023Potential and limitations of random Fourier features for dequantizing quantum machine learningcited by 22
- 2014A la Carte - Learning Fast Kernelscited by 18
- 2021Nonlinear transformation of complex amplitudes via quantum singular value transformationcited by 9
- 2024Inference, interference and invariance: How the Quantum Fourier Transform can help to learn from datacited by 5
- 2025Spectral Bias in Variational Quantum Machine Learningcited by 5
- 2024The state hidden subgroup problem and an efficient algorithm for locating unentanglementcited by 3
- 2026Probabilistic modeling over permutations using quantum computerscited by 1
Built on by
Citing papers per year: 2026: 3.
3 papers.