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 Zappala

doi:10.1016/j.neunet.2022.05.028

Quantum Neural Networks and Topological Quantum Field Theories

Neural Netw. 2022 Sep:153:164-178. doi: 10.1016/j.neunet.2022.05.028. Epub 2022 Jun 7.

Authors

Affiliations

¹ Center for Field Theory and Particle Physics & Department of Physics, Fudan University, Jingwan campus, Jingsan Rd, 200433 Shanghai, China; Laboratori Nazionali di Frascati INFN, Via Enrico Fermi, 54, 00044, Frascati (Rome), Italy. Electronic address: marciano@fudan.edu.cn.
² College of Design and Innovation, Tongji University, 281 Fuxin Rd, 200092 Shanghai, China. Electronic address: deenchen@tongji.edu.cn.
³ College of Design and Innovation, Tongji University, 281 Fuxin Rd, 200092 Shanghai, China; Institute for Computing Applications "Mario Picone", Italy National Research Council, Via dei Taurini, 19, 00185, Rome, Italy. Electronic address: fabrocini@tongji.edu.cn.
⁴ Allen Discovery Center, Tufts University, 200 College Avenue, 02155 Medford, MA, USA. Electronic address: fieldsres@gmail.com.
⁵ Department of Chemical and Pharmaceutical Sciences, University of Trieste, Via Giorgieri, 1, 34127 Trieste, Italy. Electronic address: enrico.greco@live.it.
⁶ Department of Physics, Xi'an Jiaotong-Liverpool University, 111 Ren'ai Rd, 215123 Suzhou, China. Electronic address: niels.gresnigt@xjtlu.edu.cn.
⁷ College of Design and Innovation, Tongji University, 281 Fuxin Rd, 200092 Shanghai, China. Electronic address: jinklub_krid@tongji.edu.cn.
⁸ Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, 1088 Xueyuan Avenue, 518055 Shenzhen, China. Electronic address: lulli@sustech.edu.cn.
⁹ College of Design and Innovation, Tongji University, 281 Fuxin Rd, 200092 Shanghai, China. Electronic address: kostas@tongji.edu.cn.
¹⁰ Yale School of Medicine, Yale University, New Haven, 06510 CT, USA. Electronic address: emanuele.zappala@yale.edu.

PMID: 35724478
DOI: 10.1016/j.neunet.2022.05.028

Abstract

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.

Keywords: Graph neural networks; Quantum amplitude classifiers; Quantum perceptron; Topological quantum field theory; Topological quantum neural networks.

MeSH terms

Machine Learning
Neural Networks, Computer*
Quantum Theory*