Improved Handwritten Digit Recognition using Quantum K-Nearest Neighbor Algorithm

Handwritten numeral recognition is a technology for automatic recognition and classification of handwritten numeral input through machine learning model. This is widely used in postal code digital automatic system to sort letters. The classical k-nearest neighbor algorithm is used in the traditional digital recognition training model. The recognized digital image classification is obtained through similarity measure or calculation and K value selection. Nonetheless, as the applied data volume exceeds a certain threshold, the time complexity of the model increases exponentially upon the similarity measure and K value search. This condition makes it hard to apply the model universally. In this paper, we introduce quantum computing, that is where digital image information is stored in the quantum state, and its similarity is calculated in parallel. Also, the most similar K points are obtained through the Grover algorithm. The theoretical analysis of the proposed improved algorithm shows that, handwritten numeral recognition based on quantum k-neighbor algorithm can improved upon time complexity of ORkM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathrm{O}\left(\mathrm{R}\sqrt{kM}\right) $$\end{document} of the existing algorithm.