Consistent Sampling With Smoothed Quantum Walk

This paper introduces a novel sampling technique based on the dynamics of a 2-state Quantum Walk (QW) in a one-dimensional space. By leveraging concepts from nonparametric statistics, specifically the kernel smoothing method, our approach addresses two key challenges in Quantum Walk sampling: discontinuities in sampling distributions and potential inaccuracies in limiting distributions. Our innovative method effectively mitigates these issues, leading to significant improvements in density estimation and sampling efficacy compared to traditional Quantum Walk distributions and sampling techniques.