EPJ Web Conf.
Volume 198, 2019Quantum Technology International Conference 2018 (QTech 2018)
|Number of page(s)||11|
|Published online||15 January 2019|
Quantum computing and the brain: quantum nets, dessins d’enfants and neural networks
German Aerospace Center, Rosa-Luxemburg-Str. 2, 10178 Berlin, Germany
* e-mail: firstname.lastname@example.org
Published online: 15 January 2019
In this paper, we will discuss a formal link between neural networks and quantum computing. For that purpose we will present a simple model for the description of the neural network by forming sub-graphs of the whole network with the same or a similar state. We will describe the interaction between these areas by closed loops, the feedback loops. The change of the graph is given by the deformations of the loops. This fact can be mathematically formalized by the fundamental group of the graph. Furthermore the neuron has two basic states |0〉 (ground state) and |1〉 (excited state). The whole state of an area of neurons is the linear combination of the two basic state with complex coefficients representing the signals (with 3 Parameters: amplitude, frequency and phase) along the neurons. If something changed in this area, we need a transformation which will preserve this general form of a state (mathematically, this transformation must be an element of the group S L(2; C)). The same argumentation must be true for the feedback loops, i.e. a general transformation of states along the feedback loops is an assignment of this loop to an element of the transformation group. Then it can be shown that the set of all signals forms a manifold (character variety) and all properties of the network must be encoded in this manifold. In the paper, we will discuss how to interpret learning and intuition in this model. Using the Morgan-Shalen compactification, the limit for signals with large amplitude can be analyzed by using quasi-Fuchsian groups as represented by dessins d’enfants (graphs to analyze Riemannian surfaces). As shown by Planat and collaborators, these dessins d’enfants are a direct bridge to (topological) quantum computing with permutation groups. The normalization of the signal reduces to the group S U(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 networks. Formally we will obtain a link between machine learning and Quantum computing.
© The Authors, published by EDP Sciences, 2019
This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.