Quantum-enhanced maximum-likelihood identification

• Main Author: Chong, Bi Qi
• Other Authors: Gu Mile
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2024
• Subjects: Physics; Quantum computing
• Online Access: https://hdl.handle.net/10356/175655
• Institution: Nanyang Technological University

A quantum state is in a superposition of its eigenstates. When measured in that eigenbasis, the quantum state will collapse into one of the eigenstates depending on the probability amplitude of each eigenstate. Maximum likelihood identification (MLI), which is to determine the eigenstate with the highest probability amplitude is important in areas such as quantum sensing and quantum error corrections. The straight forward way to determine the most dominant eigenvector is to simply measure the state multiple times. However, this method does not have any quantum advantage, therefore it can be potentially sped up by some protocol. In this project, we analyzed the Balint Protocol and Quantum Exploration Algorithms for Multi-Armed Bandits and extended them into the problem of MLI. We also compiled the necessary modifications for the implementation of these algorithms into MLI. We then implement some simple cases of these algorithms with the Qiskit library, and analysed the theoretical bounds of the performance of these algorithm in the MLI setting.