Quantum advantages for image filtering on images with efficient encoding and lower-bounded signal-to-noise ratio  

作　　者：Zidong Cui Shan Jin Akira Sone Xiaoting Wang 

机构地区：[1]Institute of Fundamental and Frontier Sciences,University of Electronic Science and Technology of China,Chengdu 610051,China [2]Key Laboratory of Quantum Physics and Photonic Quantum Information,Ministry of Education,University of Electronic Science and Technology of China,Chengdu 611731,China [3]Department of Physics,University of Massachusetts,Boston 02125,USA

出　　处：《Science China(Physics,Mechanics & Astronomy)》2024年第9期2-12,共11页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.92265208);the National Key R&D Program of China(Grant No.2018YFA0306703);startup funding supported by the University of Massachusetts,Boston。

摘　　要：Quantum image processing has long been a fascinating field,but establishing the existence of quantum speedup for all images remains challenging.In this study,we aim to identify a subset of images for which a quantum algorithm can be developed with a guaranteed advantage.Specifically,we present a quantum image filtering algorithm that exhibits an exponential speedup for efficiently encoded images with a lower-bounded signal-to-noise ratio.Our approach relies on a fixed-point Grover's search to emulate the effect of Hadamard multiplication with the filtering function.To demonstrate its effectiveness,we apply our method to three typical filtering problems.Additionally,we emphasize the significance of the efficient-encoding assumption by illustrating that the quantum speedup may diminish for images lacking efficient encoding.Our work underscores the importance of exploring image types and features to realize potential quantum advantages in image processing.

关 键 词：quantum computing quantum image filtering quantum speedup 

分 类 号：O413[理学—理论物理] TP391.41[理学—物理]