Quantum Information Processing

, Volume 15, Issue 9, pp 3543–3572 | Cite as

Quantum image matching



Quantum image processing (QIP) means the quantum-based methods to speed up image processing algorithms. Many quantum image processing schemes claim that their efficiency is theoretically higher than their corresponding classical schemes. However, most of them do not consider the problem of measurement. As we all know, measurement will lead to collapse. That is to say, executing the algorithm once, users can only measure the final state one time. Therefore, if users want to regain the results (the processed images), they must execute the algorithms many times and then measure the final state many times to get all the pixels’ values. If the measurement process is taken into account, whether or not the algorithms are really efficient needs to be reconsidered. In this paper, we try to solve the problem of measurement and give a quantum image matching algorithm. Unlike most of the QIP algorithms, our scheme interests only one pixel (the target pixel) instead of the whole image. It modifies the probability of pixels based on Grover’s algorithm to make the target pixel to be measured with higher probability, and the measurement step is executed only once. An example is given to explain the algorithm more vividly. Complexity analysis indicates that the quantum scheme’s complexity is \(O(2^{n})\) in contradistinction to the classical scheme’s complexity \(O(2^{2n+2m})\), where m and n are integers related to the size of images.


Quantum image processing Quantum computation Quantum image matching 



The authors thank Prof. Sabre Kais and Ph.d. Student Yudong Cao at Purdue University for their valuable suggestions.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.College of Computer ScienceBeijing University of TechnologyBeijingChina
  2. 2.School of Computer and Information TechnologyBeijing Jiaotong UniversityBeijingChina
  3. 3.College of SciencePurdue UniversityWest LafayetteUSA
  4. 4.Beijing Key Laboratory of Trusted ComputingBeijingChina
  5. 5.National Engineering Laboratory for Critical Technologies of Information Security Classified ProtectionBeijingChina

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