Zhongtian Dong
(Department of Physics & Astronomy, University of Kansas, Lawrence, KS 66045, USA)
Marçal Comajoan Cara
(Department of Signal Theory and Communications, Polytechnic University of Catalonia, 08034 Barcelona, Spain)
Gopal Ramesh Dahale
(Indian Institute of Technology Bhilai, Kutelabhata, Khapri, District-Durg, Chhattisgarh 491001, India)
Roy T. Forestano
(Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA)
Sergei Gleyzer
(Department of Physics & Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA)
Daniel Justice
(Software Engineering Institute, Carnegie Mellon University, 4500 Fifth Avenue, Pittsburgh, PA 15213, USA)
Kyoungchul Kong
(Department of Physics & Astronomy, University of Kansas, Lawrence, KS 66045, USA)
Tom Magorsch
(Physik-Department, Technische Universität München, James-Franck-Str. 1, 85748 Garching, Germany)
Konstantin T. Matchev
(Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA)
Katia Matcheva
(Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA)
Eyup B. Unlu
(Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA)
Journal: Axioms
•
• MDPI AG
• ISSN: 2075-1680
Abstract
This paper presents a comparative analysis of the performance of Equivariant Quantum Neural Networks (EQNNs) and Quantum Neural Networks (QNNs), juxtaposed against their classical counterparts: Equivariant Neural Networks (ENNs) and Deep Neural Networks (DNNs). We evaluate the performance of each network with three two-dimensional toy examples for a binary classification task, focusing on model complexity (measured by the number of parameters) and the size of the training dataset. Our results show that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub><mo>×</mo><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> EQNN and the QNN provide superior performance for smaller parameter sets and modest training data samples.