Freiburg 2019 – wissenschaftliches Programm

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FM: Fall Meeting

FM 79: Entanglement: Neural Networks for Many-Body Dynamics

FM 79.3: Talk

Donnerstag, 26. September 2019, 14:30–14:45, 2004

Many body quantum states and neural networks — •Felix Behrens, Stefanie Czischek, Martin Gärttner, and Thomas Gasenzer — Kirchhoff Institute for Physics Heidelberg

our goal is to represent quantum systems with neaural networks. doing this in a naive way, two major problems which naturally arise are inherent for quantum systems. these are the complex valued probability amplitudes and the exponential scaling of the hilbert space.

operator valued measures (povm) are the tool to map density matrices of abritrary quantum systems to probability distributions in an invertable way. after performing povm measurements, all degrees of freedom are positive real valued numbers. these probabilities are the fundamental link to machine learning systems in general and restricted boltzmann machines (rbm) in our investigations. using these systems (rbm) as generative models for informationally complete quantum measurements feature approximations with polynomially many parameters and allow efficient calculation of expectation values. in this talk, I will present a way how to map the time evolution of a density matrix under a given hamiltonian to a linear evolution equation for the probability distribution in the context of povm.