The Gell-Mann feature map of qutrits and its applications in classification tasks

TL;DR

This paper explores the use of qutrits and the Gell-Mann feature map in quantum machine learning, demonstrating potential for improved classification tasks with low-depth quantum circuits.

Contribution

It introduces the Gell-Mann feature map for qutrits and compares its performance with qubit and classical maps in classification tasks.

Findings

Gell-Mann feature map encodes information in an 8-dimensional Hilbert space.

Qutrit-based maps show potential advantages over qubit and classical maps.

Analysis of circuit architectures and optimization techniques for qutrit systems.

Abstract

Recent advancements in quantum hardware have enabled the realization of high-dimensional quantum states. This work investigates the potential of qutrits in quantum machine learning, leveraging their larger state space for enhanced supervised learning tasks. To that end, the Gell-Mann feature map is introduced which encodes information within an $8$-dimensional Hilbert space. The study focuses on classification problems, comparing Gell-Mann feature map with maps generated by established qubit and classical models. We test different circuit architectures and explore possibilities in optimization techniques. By shedding light on the capabilities and limitations of qutrit-based systems, this research aims to advance applications of low-depth quantum circuits.