Regensburg 2022 – wissenschaftliches Programm
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QI: Fachverband Quanteninformation
QI 6: Quantum Information: Concepts and Methods
QI 6.2: Vortrag
Dienstag, 6. September 2022, 10:00–10:15, H9
Learning variable quantum processes — Marco Fanizza1, Yihui Quek2, and •Matteo Rosati3 — 1FT: IFQ, Universitat Autonoma de Barcelona, 08193 Bellaterra (Barcelona) Spain — 2Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany — 3Electrical Engineering and Computer Science, Technische Universität Berlin, 10587 Berlin, Germany
Much of the current research on characterizing quantum processes via statistical learning theory assumes a highly controlled learning setting. Typically, the learner is allowed to use the unknown process as a black-box that may be applied to well-crafted inputs. In this work, we relax this assumption. How hard is it to learn a quantum process observed ‘in-the-wild’, without control over the inputs? This is the case, for instance, in learning astronomical processes induced by random celestial events, Hamiltonians at variable temperature and biological processes triggered by mechanisms which we can observe but not control. We reformulate this problem as one where a learner has access to a source that outputs classical-quantum states ∑x p(x)|x⟩⟨ x|⊗ψ(x) where ψ is the unknown process mapping an input classical random variable x to an output quantum state. The goal is to learn ψ. When ψ is drawn from a class of functions C, we show that the complexity of this task scales polynomially in a combinatorial dimension of C (a measure of its effective size) that we define, and further give algorithms that achieve this complexity. We show, for the first time to our knowledge, that quantum states and processes can be learned efficiently even when identical repetitions of the same experiment are not possible.