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 2.9: Vortrag

Montag, 27. März 2023, 12:45–13:00, HSZ 03

Time-dependent variational principle for quantum and classical dynamics — •Moritz Reh¹, Markus Schmitt², and Martin Gärttner^{1, 3, 4} — ¹Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany — ²Institut für Theoretische Physik, Universität zu Köln, 50937 Köln, Germany — ³Physikalisches Institut, Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany — ⁴Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany

The solution of many-body quantum dynamics is a challenging feat due to the curse of dimensionality, hindering the exploration of dynamics beyond a mediocre number of qubits. Neural Networks can variationally approximate the state of interest and therefore present a promising tool as they allow to efficiently represent the quantum state at the expense of truncating the Hilbert space.

We present such a scheme that is aimed at solving dissipative quantum dynamics using a probabilistic framework, i.e. the so-called POVM-formalism and demonstrate it for spin chains of up to 40 spins. We then show that the generality of the approach allows us to translate this formalism directly to the case of partial differential equations in high dimensions, defeating the exponential growth of grid cells when adding dimensions.