Quantum-enhanced maximum-likelihood identification
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 h...
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| Format: | Final Year Project |
| Language: | English |
| Published: |
Nanyang Technological University
2024
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| Online Access: | https://hdl.handle.net/10356/175655 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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. |
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