Freiburg 2019 – wissenschaftliches Programm

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FM: Fall Meeting

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

FM 79.6: Talk

Donnerstag, 26. September 2019, 15:00–15:15, 2004

Quantum computing and neural networks: a topological approach — •Torsten Asselmeyer-Maluga — German Aerospace Center (DLR), Rosa-LUxemburg-Str 2, 10178 Berlin, Germany

A neural network but also the brain can be seen as a dynamical graph of neurons with electrical signals having amplitude, frequency and phase. Because of the complexity of the graph, it is hopeless to include the whole graph. Instead we form areas of neurons having the same state (ground state or excited state). We describe the interaction between these areas by closed loops, the feedback loops. The change of the graph is given by deformations of the loops. At first view, the neuron area interaction as represented by loops cannot be neglected. Then it can be shown that the set of all signals forms a manifold (character variety). In the talk, we will discuss how to interpret learning and intuition in this model. Using the Morgan-Shalen compactification, the limit for large graphs can be analyzed by using quasi-Fuchsian groups as represented by dessins d'enfants (graphs to analyze Riemannian surfaces). These dessins d'enfants are a direct bridge to (topological) Quantum computing with permutation groups. The normalization of the signal reduces the group to SU(2) and the whole model to a quantum network. Then we have a direct connection to quantum circuits. This network can be transformed into operations on tensor products of states. Formally, we obtained a link between machine learning and Quantum computing.

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