Analysis and improvement of the quantum image matching

We investigate the quantum image matching algorithm proposed by Jiang et al. (Quantum Inf Process 15(9):3543–3572, 2016). Although the complexity of this algorithm is much better than the classical exhaustive algorithm, there may be an error in it: After matching the area between two images, only the pixel at the upper left corner of the matched area played part in following steps. That is to say, the paper only matched one pixel, instead of an area. If more than one pixels in the big image are the same as the one at the upper left corner of the small image, the algorithm will randomly measure one of them, which causes the error. In this paper, an improved version is presented which takes full advantage of the whole matched area to locate a small image in a big image. The theoretical analysis indicates that the network complexity is higher than the previous algorithm, but it is still far lower than the classical algorithm. Hence, this algorithm is still efficient.