{"title":"在具有高效编码和较低信噪比限制的图像上进行图像滤波的量子优势","authors":"Zidong Cui, Shan Jin, Akira Sone, Xiaoting Wang","doi":"10.1007/s11433-024-2391-8","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":774,"journal":{"name":"Science China Physics, Mechanics & Astronomy","volume":null,"pages":null},"PeriodicalIF":6.4000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quantum advantages for image filtering on images with efficient encoding and lower-bounded signal-to-noise ratio\",\"authors\":\"Zidong Cui, Shan Jin, Akira Sone, Xiaoting Wang\",\"doi\":\"10.1007/s11433-024-2391-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>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.</p></div>\",\"PeriodicalId\":774,\"journal\":{\"name\":\"Science China Physics, Mechanics & Astronomy\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":6.4000,\"publicationDate\":\"2024-08-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Science China Physics, Mechanics & Astronomy\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11433-024-2391-8\",\"RegionNum\":1,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Science China Physics, Mechanics & Astronomy","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11433-024-2391-8","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Quantum advantages for image filtering on images with efficient encoding and lower-bounded signal-to-noise ratio
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.
期刊介绍:
Science China Physics, Mechanics & Astronomy, an academic journal cosponsored by the Chinese Academy of Sciences and the National Natural Science Foundation of China, and published by Science China Press, is committed to publishing high-quality, original results in both basic and applied research.
Science China Physics, Mechanics & Astronomy, is published in both print and electronic forms. It is indexed by Science Citation Index.
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