Qutrit-based quantum algorithms: exploring the potential of three state quantum systems
QIntern 2023
Abstract
This project aims to investigate and develop a deeper understanding of qutrits as a generalization of qubits in quantum computing. While qubits have been at the forefront of quantum computing research, we believe qutrits hold untapped potential. By generalizing established quantum algorithms like the Deutsch-Jozsa and Grover’s algorithms to a qutrit basis, we aim to highlight the advantages and nuances of qutrit implementation, with a particular focus on efficient Toffoli gate decomposition. A similar work for the Bernstein–Vazirani algorithm can be found at https://pennylane.ai/qml/demos/tutorial_qutrits_bernstein_vazirani.html. The scope of work includes (1) a comprehensive review of qutrit-based quantum computing and its underlying principles. (2) analysis of existing qubit-based quantum algorithms (such as Deutsch–Jozsa and Grover’s algorithms) and their potential qutrit-based implementations. (3) Experimentation and implementation of qutrit-based quantum algorithms, focusing on an efficient decomposition of the Toffoli gate. (4) Comparative study of qubit and qutrit implementations and the efficiency gains achieved with qutrits.
