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Quantum image matching

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Abstract

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.

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Acknowledgments

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

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Authors and Affiliations

  1. College of Computer Science, Beijing University of Technology, Beijing, 100124, China

    Nan Jiang & Yijie Dang

  2. School of Computer and Information Technology, Beijing Jiaotong University, Beijing, 100044, China

    Jian Wang

  3. College of Science, Purdue University, West Lafayette, IN, 47905, USA

    Nan Jiang & Jian Wang

  4. Beijing Key Laboratory of Trusted Computing, Beijing, 100124, China

    Nan Jiang

  5. National Engineering Laboratory for Critical Technologies of Information Security Classified Protection, Beijing, 100124, China

    Nan Jiang

Authors
  1. Nan Jiang
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  2. Yijie Dang
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  3. Jian Wang
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Corresponding author

Correspondence to Jian Wang.

Additional information

This work is supported by the National Natural Science Foundation of China under Grants No. 61502016, the Fundamental Research Funds for the Central Universities under Grants No. 2015JBM027, and the Graduate Technology Fund of BJUT under Grants No. ykj-2015-11719.

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Jiang, N., Dang, Y. & Wang, J. Quantum image matching. Quantum Inf Process 15, 3543–3572 (2016). https://doi.org/10.1007/s11128-016-1364-2

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  • DOI: https://doi.org/10.1007/s11128-016-1364-2

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