Superpositional Quantum Network Topologies

Abstract:

We introduce superposition-based quantum networks composed of (i) the classical perceptron model of multilayered, feedforward neural networks and (ii) the algebraic model of evolving reticular quantum structures as described in quantum gravity. The main feature of this model is moving from particular neural topologies to a quantum metastructure which embodies many differing topological patterns. Using quantum parallelism, training is possible on superpositions of different network topologies. As a result, not only classical transition functions, but also topology becomes a subject of training. The main feature of our model is that particular neural networks, with different topologies, are quantum states. We consider high-dimensional dissipative quantum structures as candidates for implementation of the model.

Keywords: neural networks; quantum topology

Document Type: Research article

DOI: 10.1023/B:IJTP.0000049008.51567.ec

Affiliations: 1: Quantum Information Science and Technology Project, ATIP, Tokyo, Japan, and Universiteit van Amsterdam, The Netherlands;, Email: altmanc@admiral.umsl.edu 2: Instytut Matematyki, Uniwersytet Gdaski, Wita Stwosza 57, 80-952 Gdask, Poland, and Center Leo Apostel of the Vrije Universiteit Brussels (VUB), Krijgskundestraat 33, 1160 Brussel ski, Wita Stwosza 57, 80-952 Gdask, Poland, and Center Leo Apostel of the Vrije Universiteit Brussels (VUB), Krijgskundestraat 33, 1160 Brussel "> 3: Friedmann Lab. for Theoretical Physics, SPb UEF, Griboyedova 30–32, 191023, St. Petersburg, Russia