Berlin 2024 – scientific programme
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QI: Fachverband Quanteninformation
QI 9: Quantum Machine Learning and Classical Simulability
QI 9.5: Talk
Tuesday, March 19, 2024, 10:45–11:00, HFT-FT 101
Information-theoretic generalization bounds for learning from quantum data — •Matthias C. Caro1,2, Tom Gur3, Cambyse Rouzé4,5, Daniel Stilck França6, and Sathyawageeswar Subramanian3,7 — 1Dahlem Center for Complex Quantum Systems, FU Berlin — 2IQIM, Caltech — 3Department of Computer Science and Technology, University of Cambridge — 4Inria, Télécom Paris - LTCI, Institut Polytechnique de Paris, Palaiseau, France — 5Zentrum Mathematik, TU München — 6Univ Lyon, ENS Lyon, UCBL, CNRS, Inria, LIP, F-69342, Lyon Cedex 07, France — 7Department of Computer Science, University of Warwick
Learning tasks play an increasingly prominent role in quantum information and computation. However, the many directions of quantum learning theory have so far evolved separately. We propose a general mathematical formalism for describing quantum learning by training on classical-quantum data and then testing how well the learned hypothesis generalizes to new data. In this framework, we prove bounds on the expected generalization error of a quantum learner in terms of classical and quantum information-theoretic quantities measuring how strongly the learner's hypothesis depends on the specific data seen during training. To achieve this, we use tools from quantum optimal transport and quantum concentration inequalities. Our framework encompasses and gives intuitively accessible generalization bounds for a variety of quantum learning scenarios. Thereby, our work lays a foundation for a unifying quantum information-theoretic perspective on quantum learning.