A quantum search algorithm of two-dimensional convex hull

Despite the rapid development of quantum research in recent years, there is very little research in computational geometry. In this paper, to achieve the convex hull of a point set in a quantum system, a quantum convex hull algorithm based on the quantum maximum or minimum searching algorithm (QUSSMA) is proposed. Firstly, the novel enhanced quantum representation of digital images is employed to represent a group of point set, and then the QUSSMA algorithm and vector operation are used to search the convex hull of the point set. In addition, the algorithm is simulated and compared with the classical algorithm. It is concluded that the quantum algorithm accelerates the classical algorithm when the ${M}_{p}$ value of the convex hull point is under a certain condition.