Fixed-point quantum continuous search algorithm with optimal query complexity
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913704641036288 |
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| author | Jin, Shan Huang, Yuhan Wu, Shaojun Zhou, Guanyu Zou, Chang-Ling Sun, Luyan Wang, Xiaoting |
| author_facet | Jin, Shan Huang, Yuhan Wu, Shaojun Zhou, Guanyu Zou, Chang-Ling Sun, Luyan Wang, Xiaoting |
| contents | Continuous search problems (CSPs), which involve finding solutions within a continuous domain, frequently arise in fields such as optimization, physics, and engineering. Unlike discrete search problems, CSPs require navigating an uncountably infinite space, presenting unique computational challenges. In this work, we propose a fixed-point quantum search algorithm that leverages continuous variables to address these challenges, achieving a quadratic speedup. Inspired by the discrete search results, we manage to establish a lower bound on the query complexity of arbitrary quantum search for CSPs, demonstrating the optimality of our approach. In addition, we demonstrate how to design the internal structure of the quantum search oracle for specific problems. Furthermore, we develop a general framework to apply this algorithm to a range of problem types, including optimization and eigenvalue problems involving continuous variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15556 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fixed-point quantum continuous search algorithm with optimal query complexity Jin, Shan Huang, Yuhan Wu, Shaojun Zhou, Guanyu Zou, Chang-Ling Sun, Luyan Wang, Xiaoting Quantum Physics Continuous search problems (CSPs), which involve finding solutions within a continuous domain, frequently arise in fields such as optimization, physics, and engineering. Unlike discrete search problems, CSPs require navigating an uncountably infinite space, presenting unique computational challenges. In this work, we propose a fixed-point quantum search algorithm that leverages continuous variables to address these challenges, achieving a quadratic speedup. Inspired by the discrete search results, we manage to establish a lower bound on the query complexity of arbitrary quantum search for CSPs, demonstrating the optimality of our approach. In addition, we demonstrate how to design the internal structure of the quantum search oracle for specific problems. Furthermore, we develop a general framework to apply this algorithm to a range of problem types, including optimization and eigenvalue problems involving continuous variables. |
| title | Fixed-point quantum continuous search algorithm with optimal query complexity |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2502.15556 |