SKM 2023 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 2: Focus Session: Physics Meets ML I – Machine Learning for Complex Quantum Systems (joint session TT/DY)
DY 2.2: Hauptvortrag
Montag, 27. März 2023, 10:00–10:30, HSZ 03
Data mining the output of quantum simulators -- from critical behavior to algorithmic complexity — •Marcello Dalmonte — Abdus Salam International Centre for Theoretical Physics, Trieste (I)
Recent experiments with quantum simulators and noisy intermediate-scale quantum devices have demonstrated unparalleled capabilities of probing many-body wave functions, via directly probing them at the single quantum level via projective measurements. However, very little is known about to interpret and analyse such huge datasets. In this talk, I will show how it is possible to provide such characterisation of many-body quantum hardware via a direct and assumption-free data mining. The core idea of this programme is the fact that the output of quantum simualtors and computers can be construed as a very high-dimensional manifold. Such manifold can be characterised via basic topological concepts, in particular, by their intrinsic dimension. Exploiting state of the art tools in non-parametric learning, I will discuss theoretical results for both classical and quantum many-body spin systems that illustrate how data structures undergo structural transitions whenever the underlying physical system does, and display universal (critical) behavior in both classical and quantum mechanical cases. I will conclude with remarks on the applicability of our theoretical framework to synthetic quantum systems (quantum simulators and quantum computers), and emphasize its potential to provide a direct, scalable measure of Kolmogorov complexity of output states.