Qutrit-Based Neural Quantum Kernels for Classification Tasks

This paper investigates the extension of Neural Quantum Kernels (NQKs) from qubit-based systems to qudit-based systems, specifically focusing on qutrits (d=3). NQKs are a hybrid machine learning framework where a quantum neural network (QNN) is pretrained to learn a task-adapted embedding, which is then frozen to define a quantum kernel for subsequent classification. The authors explore how moving to higher-dimensional Hilbert spaces (SU(3)) allows for richer data embeddings and more natural handling of multiclass classification tasks. They perform a systematic ablation study on key design choices, including the number of encoded features, the number of qutrits, the kernel construction method (1-to-n vs. n-to-n), and the specific parameterization of SU(3) unitaries.

The study demonstrates that qutrit-based NQKs generally improve classification performance compared to their qubit-based QNN counterparts. By utilizing the eight generators of SU(3), the qutrit models can incorporate more features per subsystem, effectively overcoming the structural bottlenecks inherent in qubit-based architectures. The authors find that while scaling the system size and feature budget typically enhances performance, these gains are not infinite and often saturate depending on the specific dataset. Furthermore, the choice of how to parameterize the SU(3) unitaries is shown to be a critical design factor, as different representations lead to significant variations in optimization behavior and model expressivity.

This work provides a practical roadmap for scaling quantum machine learning models beyond the standard qubit paradigm. By showing that qudit systems can be integrated into existing NQK frameworks, the paper highlights a viable path toward exploiting complex data structures that are better suited for higher-dimensional quantum systems. The findings suggest that qudits are not merely a theoretical generalization but a functional tool for improving the performance and efficiency of quantum-enhanced classification in the NISQ era.