Histogram algorithm and its circuit design based on parallel computing for quantum video

Quantum image histogram as a preprocessing result in quantum image processing contains the gray information of the image and plays an important role in subsequent image processing. As far as we know, there are only a few results on quantum image histogram, and studies on quantum video histogram have not been conducted. So a novel histogram statistic algorithm for quantum video in terms of the idea of parallel computing is proposed in the paper. To this end, the quantum version of carry-lookahead full-adder is first devised, and based on the novel full-adder, an entirely new hierarchical quantum adder for superposition states is also devised, which not only improves the delays generated by mutual carries of classical adder, but also reduces the complexity of classical adder from O(2mxn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {O(2<^>{m}\times n)}$$\end{document} to O(m2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {O(m<^>{2})}$$\end{document}. Subsequently, in order to realize the parallel statistics of quantum video, the algorithm and circuit implementation of image stitching are also given. Finally, combining the results of image stitching and Grover's search algorithm, the quantum video histogram statistics is ultimately realized in parallel.