Comparison between Tensor Networks and Variational Quantum Classifier

arXiv (Cornell University)

Abstract

The primary objective of this paper is to conduct a comparative analysis between two Machine Learning approaches: Tensor Networks (TN) and Variational Quantum Classifiers (VQC). While both approaches share similarities in their representation of the Hilbert space using a logarithmic number of parameters, they diverge in the manifolds they cover. Thus, the aim is to evaluate and compare the expressibility and trainability of these approaches. By conducting this comparison, we can gain insights into potential areas where quantum advantage may be found. Our findings indicate that VQC exhibits advantages in terms of speed and accuracy when dealing with data, characterized by a small number of features. However, for high-dimensional data, TN surpasses VQC in overall classification accuracy. We believe that this disparity is primarily attributed to challenges encountered during the training of quantum circuits. We want to stress that in this article, we focus on only one particular task and do not conduct thorough averaging of the results. Consequently, we recommend considering the results of this article as a unique case without excessive generalization.

Authors 5

1. Artem A. Melnikov

   Terra Quantum (Switzerland)

   Affiliation as printed

   Terra Quantum AG , Kornhausstrasse 25 , 9000 St. Gallen , Switzerland

2. Michael Romanovich Perelshtein

   Terra Quantum (Switzerland)

   Affiliation as printed

   Terra Quantum AG , Kornhausstrasse 25 , 9000 St. Gallen , Switzerland

3. Reuben Brasher

   Terra Quantum (Switzerland)

   Affiliation as printed

   Terra Quantum AG , Kornhausstrasse 25 , 9000 St. Gallen , Switzerland

4. Thomas Baeck
5. Florian Neukart Aachen

   Leiden University · University of Applied Sciences Leiden · Terra Quantum (Switzerland)

   Affiliation as printed

   LIACS , Leiden University Leiden , Netherlands

   Terra Quantum AG , Kornhausstrasse 25 , 9000 St. Gallen , Switzerland