SAQNN: Spectral Adaptive Quantum Neural Network as a Universal Approximator
Not on the map. Why?
Abstract (arXiv)
Quantum machine learning (QML), as an interdisciplinary field bridging quantum computing and machine learning, has garnered significant attention in recent years. Currently, the field as a whole faces challenges due to incomplete theoretical foundations for the expressivity of quantum neural networks (QNNs). In this paper we propose a constructive QNN model and demonstrate that it possesses the universal approximation property (UAP), which means it can approximate any square-integrable function up to arbitrary accuracy. Furthermore, it supports switching function bases, thus adaptable to various scenarios in numerical approximation and machine learning. Our model has asymptotic advantages over the best classical feed-forward neural networks in terms of circuit size and achieves optimal parameter complexity when approximating Sobolev functions under L2 norm.
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 34 of its 96 references that are in the map. First posted on arXiv 10 Feb 2026.
Builds on
34 of 96 references.
References · 34
- 2017Attention Is All You Needcited by 59,932
- 2020Language Models are Few-Shot Learnerscited by 32,199
- 2020Denoising Diffusion Probabilistic Modelscited by 20,851
- 2022Training language models to follow instructions with human feedbackcited by 15,712
- 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
- 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
- 2017Quo Vadis, Action Recognition? A New Model and the Kinetics Datasetcited by 3,259
- 2020Variational Quantum Algorithmscited by 687
- 2023A Comprehensive Overview of Large Language Modelscited by 639
- 2018Barren plateaus in quantum neural network training landscapescited by 624
- 2016Error bounds for approximations with deep ReLU networkscited by 567
- 2020The power of quantum neural networkscited by 377
22 more
- 2020Power of data in quantum machine learningcited by 336
- 2020The effect of data encoding on the expressive power of variational quantum machine learning modelscited by 328
- 2021Connecting ansatz expressibility to gradient magnitudes and barren plateauscited by 180
- 2018Optimal approximation of continuous functions by very deep ReLU networkscited by 165
- 2020Deep Network Approximation for Smooth Functionscited by 163
- 2018Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionalitycited by 160
- 2018Quantum generative adversarial networkscited by 128
- 2019Deep Network Approximation Characterized by Number of Neuronscited by 120
- 2021Theory of overparametrization in quantum neural networkscited by 100
- 2021Optimal Approximation Rate of ReLU Networks in terms of Width and Depthcited by 95
- 2019The phase diagram of approximation rates for deep neural networkscited by 86
- 2018Continuous-variable quantum neural networkscited by 74
- 2024Diffusion Models in Low-Level Vision: A Surveycited by 73
- 2022Optimal Approximation Rates for Deep ReLU Neural Networks on Sobolev and Besov Spacescited by 50
- 2020Universal Approximation Property of Quantum Machine Learning Models in Quantum-Enhanced Feature Spacescited by 44
- 2019Nonlinear Approximation via Compositionscited by 37
- 2022Power and limitations of single-qubit native quantum neural networkscited by 19
- 2021Sample Complexity of Learning Parametric Quantum Circuitscited by 15
- 2024On the optimal approximation of Sobolev and Besov functions using deep ReLU neural networkscited by 13
- 2023Non-asymptotic Approximation Error Bounds of Parameterized Quantum Circuitscited by 9
- 2023Implementing any Linear Combination of Unitaries on Intermediate-term Quantum Computerscited by 4
- 2024Feed-Forward Neural Networks as a Mixed-Integer Programcited by 4
Built on by
Not cited yet.