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RECENT POSTS IN THIS TOPIC

Peter Morgan: on 9/21/21 at 20:19pm UTC, wrote How much difference do you see between the classical and quantum parts of...

Jens Eisert: on 9/21/21 at 18:18pm UTC, wrote Date of seminar: 12 July 2021 - 4:00pm - 5:00pm (GST) Title: Learning...


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FQXi BLOGS
July 3, 2022

CATEGORY: Blog [back]
TOPIC: Learning classical and quantum dynamical laws from data by Jens Eisert [refresh]
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Blogger Jens Eisert wrote on Sep. 21, 2021 @ 18:18 GMT
Date of seminar: 12 July 2021 - 4:00pm - 5:00pm (GST)



Title: Learning classical and quantum dynamical laws from data



Abstract: Traditionally, physical laws are being formulated in a largely heuristic fashion and subsequently their predictions are empirically explored. Generations of physics students are being told that Hamiltonians govern the dynamics of physical systems both in the quantum and classical realm. While this is perfectly right, much less is said on how these Hamiltonian are determined or characterized in the first place. Often, a-priori knowledge of some sort is available, but then the question emerges of how one can be sure that the actual Hamiltonian is close to the anticipated one based on physical reasoning. This issue seems particularly pressing for complex systems involving many degrees of freedom, or for systems in the quantum technologies where high precision is imperative.



These basic yet profound insights motivate efforts to learn Hamiltonians - or directly physical laws - from data. In the first part of this talk, we will be concerned with new ways of learning classical dynamical laws from data. We move on to learn instances of quantum Hamiltonians from data, and show how superconducting devices as experimented with by the Google AI team can be characterized to unprecedented precision. We will see how one can set up a tensor network based and machine learning inspired way of learning quantum many-body Hamiltonians from dynamical data. If time allows, I will mention aspects of rigorously minded quantum-assisted machine learning and of the recovery of quantum processes from data. In an outlook, we will discuss further perspectives of data-driven approaches in identifying physical laws from data.



Keywords: #iaf #quantum #foundations #data

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Peter Warwick Morgan wrote on Sep. 21, 2021 @ 20:19 GMT
How much difference do you see between the classical and quantum parts of your talk, Jens? I wonder whether you think that Koopman's Hilbert space formalism for classical mechanics might help to bring them more together?

That's a somewhat leading question, as you'll know if you've seen my talk at IQOQI in March or my paper in Annals of Physics 2020. In both of those, I adopt a signal analysis approach to the interpretation of both classical and quantum mechanics, so I feel a lot of common cause with your approach and with your talk.

Koopman's Hilbert space formalism, however, is perhaps not as important as an algebraic understanding that nonabelian transformation algebras are as significant and as natural for classical measurement theory as they are for quantum measurement theory. Consequently, measurement incompatibility and contextuality need to be included as naturally as possible in any fully realized formalism for classical mechanics. [Even if we introduce noncommutativity into classical mechanics, there remain two other differences between classical and quantum mechanics, but I won't bother you with those here. I'll mention that I've discussed these ideas quite a bit with Marek Gluza, so you can ask him about them before responding here or elsewhere. In any case, Nice Talk!]

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