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$\mathbb{Z}_2\times \mathbb{Z}_2$ Equivariant Quantum Neural Networks: Benchmarking against Classical Neural Networks

Zhongtian Dong, Marçal Comajoan Cara, Gopal Ramesh Dahale, Roy T. Forestano, Sergei Gleyzer, Daniel Justice, Kyoungchul Kong, Tom Magorsch, Konstantin T. Matchev, Katia Matcheva, Eyup B. Unlu

Abstract

This paper presents a comprehensive comparative analysis of the performance of Equivariant Quantum Neural Networks (EQNN) and Quantum Neural Networks (QNN), juxtaposed against their classical counterparts: Equivariant Neural Networks (ENN) and Deep Neural Networks (DNN). We evaluate the performance of each network with two toy examples for a binary classification task, focusing on model complexity (measured by the number of parameters) and the size of the training data set. Our results show that the $\mathbb{Z}_2\times \mathbb{Z}_2$ EQNN and the QNN provide superior performance for smaller parameter sets and modest training data samples.

$\mathbb{Z}_2\times \mathbb{Z}_2$ Equivariant Quantum Neural Networks: Benchmarking against Classical Neural Networks

Abstract

This paper presents a comprehensive comparative analysis of the performance of Equivariant Quantum Neural Networks (EQNN) and Quantum Neural Networks (QNN), juxtaposed against their classical counterparts: Equivariant Neural Networks (ENN) and Deep Neural Networks (DNN). We evaluate the performance of each network with two toy examples for a binary classification task, focusing on model complexity (measured by the number of parameters) and the size of the training data set. Our results show that the EQNN and the QNN provide superior performance for smaller parameter sets and modest training data samples.
Paper Structure (5 sections, 5 equations, 6 figures, 1 table)

This paper contains 5 sections, 5 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Dataset Description
  3. Network Architectures
  4. Results
  5. Conclusions

Figures (6)

  • Figure S1: Pictorial illustration of the first dataset used in this study---the symmetric case (\ref{['eq:labelexample1']}).
  • Figure S2: Pictorial illustration of the second dataset used in this study---the anti-symmetric case (\ref{['eq:labelexample2']}).
  • Figure S3: Pictorial illustration of the third dataset used in this study---the fully anti-symmetric case (\ref{['eq:labelexample3']}).
  • Figure S5: Illustration of the quantum circuit used for EQNN at depth 1. This circuit is repeated five (ten) times with different parameters for the symmetric (anti-symmetric and fully anti-symmetric) case. The data points $(x_1, x_2)$ are loaded via angle embedding with two $R_Z$ gates, $R_Z(x_1)$ and $R_Z(x_2)$. The remaining circuits are parameterized by $R_X(\theta_1)$ and $R_Z(\theta_2)$.
  • Figure S6: ROC (left) and accuracy (right) curves for the symmetric (top), anti-symmetric (middle), and fully anti-symmetric (bottom) example.
  • ...and 1 more figures