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

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

^*Corresponding author for this work

Department of Physics

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

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.

Original language	English
Pages (from-to)	164-178
Number of pages	15
Journal	Neural Networks
Volume	153
DOIs	https://doi.org/10.1016/j.neunet.2022.05.028
Publication status	Published - Sept 2022

Keywords

Graph neural networks
Quantum amplitude classifiers
Quantum perceptron
Topological quantum field theory
Topological quantum neural networks

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10.1016/j.neunet.2022.05.028

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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.",

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T1 - Quantum Neural Networks and Topological Quantum Field Theories

AU - Marcianò, Antonino

AU - Chen, Deen

AU - Fabrocini, Filippo

AU - Fields, Chris

AU - Greco, Enrico

AU - Gresnigt, Niels

AU - Jinklub, Krid

AU - Lulli, Matteo

AU - Terzidis, Kostas

AU - Zappala, Emanuele

PY - 2022/9

Y1 - 2022/9

N2 - 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.

AB - 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.

KW - Graph neural networks

KW - Quantum amplitude classifiers

KW - Quantum perceptron

KW - Topological quantum field theory

KW - Topological quantum neural networks

UR - https://www.scopus.com/pages/publications/85132938862

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DO - 10.1016/j.neunet.2022.05.028

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AN - SCOPUS:85132938862

SN - 0893-6080

VL - 153

SP - 164

EP - 178

JO - Neural Networks

JF - Neural Networks

ER -

Quantum Neural Networks and Topological Quantum Field Theories

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Keywords

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