Abstract: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 correlation between the corresponding clustering phenomena and the model's adjustable parameters were studied. The role of control parameters in the evolution of quantum walks was 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.