Supervisors info:
ΔΗΜΗΤΡΙΟΣ ΣΥΒΡΙΔΗΣ, ΚΑΘΗΓΗΤΗΣ, ΤΜΗΜΑ ΠΛΗΡΟΦΟΡΙΚΗΣ ΚΑΙ ΤΗΛΕΠΙΚΟΙΝΩΝΙΩΝ, ΕΚΠΑ
Summary:
Quantum computers, leveraging the principles of quantum physics, have the potential to revolutionize various domains by utilizing quantum bits (qubits) that can exist in superpositions and entanglement, allowing for parallel exploration of solutions. Recent advancements in quantum hardware have enabled the realization of high-dimensional quantum states on a chip-scale platform, proposing another potential avenue.
The utilization of qudits, quantum systems with levels exceeding 2, not only offer increased information capacity, but also exhibit improved resilience against noise and errors. Experimental implementations have successfully showcased the potential of high-dimensional quantum systems in efficiently encoding complex quantum circuits, further highlighting their promise for the future of quantum computing.
In this thesis, the potential of qutrits is explored to enhance machine learning tasks in quantum computing. The expanded state space offered by qutrits enables richer data representation, capturing intricate patterns and relationships. To this end, employing the mathematical framework of SU(3), the Gell-Mann feature map is introduced to encode information within an 8-dimensional space. This empowers quantum computing systems to process and represent larger amounts of data within a single qutrit.
The primary focus of this thesis centers on classification tasks utilizing qutrits, where a comparative analysis is conducted between the proposed Gell-Mann feature map, well-established qubit feature maps, and classical machine learning models. Furthermore, optimization techniques within expanded Hilbert spaces are explored, addressing challenges such as vanishing gradients and barren plateaus landscapes.
This work explores foundational concepts and principles in quantum computing and machine learning to ensure a solid understanding of the subject. It also highlights recent advancements in quantum hardware, specifically focusing on qutrit-based systems.
The main objective is to explore the feasibility of the Gell-Mann encoding for multiclass classification in the SU(3) space, demonstrate the viability of expanded Hilbert spaces for machine learning tasks, and establish a robust foundation for working with geometric feature maps.
By delving into the design considerations and experimental setups in detail, this research aims to contribute to the broader understanding of the capabilities and limitations of qutrit-based systems in the context of quantum machine learning, contributing to the advancement of quantum computing and its applications in practical domains.
Keywords:
quantum circuits, machine learning, quantum information, classification, supervised learning, neural networks
