SAMOP 2021 – wissenschaftliches Programm
QI 2.3: Vortrag
Montag, 20. September 2021, 11:15–11:30, H5
Understanding Variational Quantum Learning Models — Matthias C. Caro1,2, Jens Eisert3,4, Elies Gil-Fuster3, •Johannes Jakob Meyer3,5, Maria Schuld6, and Ryan Sweke3 — 1Department of Mathematics, Technical University of Munich, Garching, Germany — 2Munich Center for Quantum Science and Technology (MCQST), Munich, Germany — 3Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Berlin, Germany — 4Helmholtz-Zentrum Berlin für Materialien und Energie, Berlin, Germany — 5QMATH, University of Copenhagen, Copenhagen, Denmark — 6Xanadu, 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 . 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 . These bounds can act as a guideline to select and optimize quantum learning models in a structural risk minimization approach. Based on  arXiv:2008.08605 and  arXiv:2106.03880.