Seminario del 2025
Giugno
dal giorno
25/06/2025
al giorno
27/06/2025
25/06/2025
al giorno
27/06/2025
Daniel Stilck Franca
Information‐theoretic Generalization Bounds for Learning from Quantum Data
Seminario di fisica matematica
Learning tasks are playing an increasingly central role in quantum information and computation from fundamental problems like state discrimination and metrology to quantum PAC learning and the recently proposed “shadow” variants of state tomography. Yet these various strands of quantum learning theory have largely evolved in isolation.
In this talk, we introduce a unified mathematical framework for quantum learning based on classical–quantum training data and show how to bound a quantum learner’s expected generalization error on new data. Our bounds are expressed in terms of classical and quantum information theoretic quantities that capture how strongly the learner’s hypothesis depends on the specific training data. To derive them, we develop non commutative analogues of the decoupling lemmas underlying recent classical information theoretic generalization bounds, drawing on tools from quantum optimal transport and quantum concentration inequalities.
This framework subsumes and yields intuitive generalization bounds for a variety of quantum learning scenarios including quantum state discrimination, PAC learning of quantum states or classical functions, and quantum parameter estimation laying the groundwork for a unified, information theoretic perspective on quantum learning.