Quantum image rotation by an arbitrary angle

In this paper, a novel method of quantum image rotation (QIR) based on shear transformations on NEQR quantum images is proposed. To compute the horizontal and vertical shear mappings required for rotation, we have designed quantum self-adder, quantum control multiplier, and quantum interpolation circuits as the basic computing units in the QIR implementation. Furthermore, we provide several examples of our results by presenting computer simulation experiments of QIR under 30∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$30^\circ $$\end{document}, 45∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$45^\circ $$\end{document}, and 60∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$60^\circ $$\end{document} rotation scenarios and have a discussion onto the anti-aliasing and computational complexity of the proposed QIR method.