Quantum Machine Learning with Group Structure
Seminar author:Berta Casas Font
Event date and time:04/03/2025 02:30:pm
Event location:Seminar Room, GIQ
Event contact:
Quantum Machine Learning (QML) explores how quantum computers can enhance learning tasks beyond classical capabilities. While extensive research has been conducted in recent years, identifying concrete learning advantages with quantum devices remains a challenge, especially given the limitations of current quantum hardware. Consequently, much of the focus has shifted toward theoretical insights that could guide future developments.
In this talk, I will discuss how group-theoretic methods provide a compelling framework for advancing QML. I will begin by introducing QML and variational quantum algorithms before delving into two key works that leverage group structures in learning problems. The first [1] establishes a framework for learning problems with inherent group symmetries using quantum kernels derived from unitary representations. Notably, one of the few known cases of provable learning quantum advantage falls within this paradigm [2]. The second work [3] investigates how the Quantum Fourier Transform, inspired by the Hidden Subgroup Problem, can be potentially used to infer structure from data.
By highlighting these approaches, I aim to illustrate how group-theoretic tools can provide an interesting framework for QML and the search for meaningful quantum learning algorithms.
References:
[1] Glick, J.R., Gujarati, T.P., Córcoles, A.D. et al. Covariant quantum kernels for data with group structure. Nat. Phys. 20, 479–483 (2024). https://doi.org/10.1038/s41567-023-02340-9
[2] Liu, Y., Arunachalam, S. & Temme, K. A rigorous and robust quantum speed-up in supervised machine learning. Nat. Phys. 17, 1013–1017 (2021). https://doi.org/10.1038/s41567-021-01287-z
[3] Wakeham, D., Schuld, M. Inference, interference and invariance: How the Quantum Fourier Transform can help to learn from data. arXiv:2409.00172 (2024).