| 广义 Grover 量子行走中的聚类现象 |
| A cluster phenomenon in generalized Grover’s quantum walks |
| 投稿时间：2024-12-06 修订日期：2025-02-20 |
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| 中文摘要: |
| 为探索量子行走在计量方面的应用，提出了含任意控制参数的广义Grover量子行走与分步Grover量子行走。研究了相应聚类现象和模型可调参数的关联性，具体分析了控制参数在量子行走演化中的作用，发现行走者的演化速度在参数空间的聚类分布与行走者量子态中的纠缠在参数空间的聚类分布呈现出一致性，进一步探究了不同聚类中行走者的概率分布。探讨了Grover量子行走的实验实现方案，论述了Grover量子行走在计量领域的应用，指出Grover量子行走对于实现高精度传感、拓扑序精确测量、态层析效率提升具有重要意义。研究成果为推动量子行走信息处理技术发展提供了有力支撑。 |
| 英文摘要: |
| To explore the application of quantum walks in metrology, generalized Grover quantum walks and stepwise Grover quantum walks with arbitrary control parameters are proposed. The corresponding clustering phenomena and the correlation between the model's adjustable parameters are studied. The role of control parameters in the evolution of quantum walks is analyzed, revealing a clustering phenomenon based on control parameters: the evolution speed of the walker shows consistency with the entanglement between its coin space and position space. Further investigation into the probability distribution of the walker in different clusters shows that the probability distributions in each cluster exhibit different characteristics. In some clusters, the distribution tends to be concentrated, while in others, it is more dispersed. The experimental implementation of Grover quantum walks is discussed, and the applications of Grover quantum walks in metrology are addressed, highlighting their significance in achieving high-precision sensing, topological order measurement, and enhanced state tomography efficiency. The research findings provide strong support for the development of quantum walk-based information processing technologies. |
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| 中文关键词: 量子行走 聚类 Grover搜索 关联性 演化速度 |
| 英文关键词:quantum walks clusering phenomena Grover search Correlation Evolution speed |
| 基金项目:中国国家自然科学基金（资助号：12104101）、中央高校基本科研业务费专项资金以及保密通信全国重点实验室稳定支持计划项目（2023）的支持，以及中国国家自然科学基金重大研究项目（资助号：92267110）、中国国家自然科学基金联合基金（资助号：U22B2025）和陕西省重点研发计划（资助号：2023-GHZD-42） |
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