Fixed-point quantum continuous search algorithm with optimal query complexity

Fuente: arXiv
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Main Authors: Jin, Shan, Huang, Yuhan, Wu, Shaojun, Zhou, Guanyu, Zou, Chang-Ling, Sun, Luyan, Wang, Xiaoting
Format: Preprint
Published: 2025
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_version_ 1866913704641036288
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