QSobel：A novel quantum image edge extraction algorithm

Edge extraction is an indispensable task in digital image processing. With the sharp increase in the image data, real-time problem has become a limitation of the state of the art of edge extraction algorithms.In this paper, QSobel, a novel quantum image edge extraction algorithm is designed based on the flexible representation of quantum image（FRQI） and the famous edge extraction algorithm Sobel. Because FRQI utilizes the superposition state of qubit sequence to store all the pixels of an image, QSobel can calculate the Sobel gradients of the image intensity of all the pixels simultaneously. It is the main reason that QSobel can extract edges quite fast. Through designing and analyzing the quantum circuit of QSobel, we demonstrate that QSobel can extract edges in the computational complexity of O（n2） for a FRQI quantum image with a size of2 n × 2n. Compared with all the classical edge extraction algorithms and the existing quantum edge extraction algorithms, QSobel can utilize quantum parallel computation to reach a significant and exponential speedup.Hence, QSobel would resolve the real-time problem of image edge extraction.