# SAMOP 2021 – wissenschaftliches Programm

## Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe

# QI: Fachverband Quanteninformation

## QI 2: Quantum Computing and Algorithms I

### QI 2.3: Vortrag

### Montag, 20. September 2021, 11:15–11:30, H5

**Understanding Variational Quantum Learning Models** — Matthias C. Caro^{1,2}, Jens Eisert^{3,4}, Elies Gil-Fuster^{3}, •Johannes Jakob Meyer^{3,5}, Maria Schuld^{6}, and Ryan Sweke^{3} — ^{1}Department of Mathematics, Technical University of Munich, Garching, Germany — ^{2}Munich Center for Quantum Science and Technology (MCQST), Munich, Germany — ^{3}Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Berlin, Germany — ^{4}Helmholtz-Zentrum Berlin für Materialien und Energie, Berlin, Germany — ^{5}QMATH, University of Copenhagen, Copenhagen, Denmark — ^{6}Xanadu, Toronto, ON, M5G 2C8, Canada

Finding practically relevant applications for noisy intermediate-scale quantum devices is an active frontier of quantum information research. Using them to execute parametrized quantum circuits used as learning models is a possible candidate. We show that the possible output functions of such learning models can be elegantly expressed by generalized trigonometric polynomials, whose available frequencies are determined by the spectra of the Hamiltonians used for the data encoding [1]. This approach allows for an intuitive understanding of quantum learning models and underlines the important role of data encoding in quantum machine learning. Building on this, we exploit this natural connection to give generalization bounds which explicitly take into account how a given quantum learning model is encoding the data [2]. These bounds can act as a guideline to select and optimize quantum learning models in a structural risk minimization approach. Based on [1] arXiv:2008.08605 and [2] arXiv:2106.03880.