Quantum Neural Networks and Topological Quantum Field Theories

Antonino Marcianò, Deen Chen, Filippo Fabrocini*, Chris Fields, Enrico Greco*, Niels Gresnigt, Krid Jinklub, Matteo Lulli, Kostas Terzidis, Emanuele Zappalà

Neural Networks, Volume 153, September 2022, Pages 164-178
DOI: 10.1016/j.neunet.2022.05.028

Our work intends to show that: (1) Quantum Neural Networks (QNNs) can be mapped onto spin-networks, with the consequence that the level of analysis of their operation can be carried out on the side of Topological Quantum Field Theory (TQFT); (2) A number of Machine Learning (ML) key-concepts can be rephrased by using the terminology of TQFT. Our framework provides as well a working hypothesis for understanding the generalization behavior of DNNs, relating it to the topological features of the graph structures involved.

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