Sparse Optimization Techniques: Applications in Quantum Computing and Beyond in Physics
量子計算及其他物理應用中的稀疏優化技術探索
Student thesis: Doctoral Thesis
Author(s)
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Detail(s)
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| Award date | 27 Aug 2024 |
Link(s)
| Permanent Link | https://scholars.cityu.edu.hk/en/theses/theses(739b7473-9888-49ac-b274-9a08a08f9c5e).html |
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| Other link(s) | Links |
Abstract
This thesis aims to study various types of sparse optimization techniques and investigate their applications in the fields of quantum computing and various physics-related domains. The primary objective is to develop efficient algorithms capable of solving diverse sparse optimization problems while considering additional constraints arising from the underlying physical properties. The research focuses on different optimization techniques that are applied to solve optimization problems with specific constraints based on the targeted models.
The thesis begins by introducing the concept of sparsity and exploring various algorithms and applications. Chapters 3 and 4 focus on optimization techniques, particularly addressing group sparsity and clustering sparsity problems. Optimization algorithms are developed to enhance the efficiency and accuracy of solving problems with structured rows and performing clustering analysis. These algorithms enable efficient handling of large-scale datasets and facilitate the extraction of meaningful patterns.
To investigate the application of sparsity in physics, this thesis delves into the field of quantum state transformation, demonstrating the merit of sparse optimization techniques in addressing the challenges posed by sparse optimization and incorporating physical constraints. In Chapter 5, an optimization algorithm based on ADMM is introduced to search for sparse transformation matrices, presenting a new approach to quantum state transformations. The effectiveness of the algorithm is demonstrated through experiments and analysis. Finally, this thesis concludes by discussing the encountered challenges in these fields and exploring potential avenues for further advancements.
The research presented in this thesis contributes to the advancement of sparse optimization techniques in quantum computing and physics-related domains. It provides valuable insights and methodologies for efficiently solving diverse optimization problems while considering the unique constraints and requirements arising from the underlying physical properties.
The thesis begins by introducing the concept of sparsity and exploring various algorithms and applications. Chapters 3 and 4 focus on optimization techniques, particularly addressing group sparsity and clustering sparsity problems. Optimization algorithms are developed to enhance the efficiency and accuracy of solving problems with structured rows and performing clustering analysis. These algorithms enable efficient handling of large-scale datasets and facilitate the extraction of meaningful patterns.
To investigate the application of sparsity in physics, this thesis delves into the field of quantum state transformation, demonstrating the merit of sparse optimization techniques in addressing the challenges posed by sparse optimization and incorporating physical constraints. In Chapter 5, an optimization algorithm based on ADMM is introduced to search for sparse transformation matrices, presenting a new approach to quantum state transformations. The effectiveness of the algorithm is demonstrated through experiments and analysis. Finally, this thesis concludes by discussing the encountered challenges in these fields and exploring potential avenues for further advancements.
The research presented in this thesis contributes to the advancement of sparse optimization techniques in quantum computing and physics-related domains. It provides valuable insights and methodologies for efficiently solving diverse optimization problems while considering the unique constraints and requirements arising from the underlying physical properties.
- sparse, quantum
