Skip to main content
Log in

NEQR: a novel enhanced quantum representation of digital images

Quantum Information Processing Aims and scope Submit manuscript

Abstract

Quantum computation is becoming an important and effective tool to overcome the high real-time computational requirements of classical digital image processing. In this paper, based on analysis of existing quantum image representations, a novel enhanced quantum representation (NEQR) for digital images is proposed, which improves the latest flexible representation of quantum images (FRQI). The newly proposed quantum image representation uses the basis state of a qubit sequence to store the gray-scale value of each pixel in the image for the first time, instead of the probability amplitude of a qubit, as in FRQI. Because different basis states of qubit sequence are orthogonal, different gray scales in the NEQR quantum image can be distinguished. Performance comparisons with FRQI reveal that NEQR can achieve a quadratic speedup in quantum image preparation, increase the compression ratio of quantum images by approximately 1.5X, and retrieve digital images from quantum images accurately. Meanwhile, more quantum image operations related to gray-scale information in the image can be performed conveniently based on NEQR, for example partial color operations and statistical color operations. Therefore, the proposed NEQR quantum image model is more flexible and better suited for quantum image representation than other models in the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

References

  1. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  2. Feynman, R.: Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982)

    Article  MathSciNet  Google Scholar 

  3. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. Proceeding of 35th Annual Symposium Foundations of Computer Science, IEEE Computer Soc. Press, Los Almitos, CA, pp. 124–134 (1994)

  4. Grover, L.: A fast quantum mechanical algorithm for database search. Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, pp. 212–219 (1996)

  5. Gonzalez, Rafael C., Woods, Richard E., Eddins, Steven L.: Digital Image Processing. Publishing House of Electronics Industry, Beijing (2002)

    Google Scholar 

  6. Venegas-Andraca, S.E., Bose, S.: Storing, processing and retrieving an image using quantum mechanics. Proceeding of the SPIE Conference Quantum Information and Computation, pp. 137–147 (2003)

  7. Venegas-Andraca, S.E., Ball, J.L., Burnett, K., Bose, S.: Processing images in entangled quantum systems. Quantum Inform. Process. 9, 1–11 (2010)

    Article  Google Scholar 

  8. Latorre, J.I.: Image compression and entanglement. arXiv:quant-ph/0510031 (2005)

  9. Le, P.Q., Dong, F., Hirota, K.: A flexible representation of quantum images for polynomial preparation, image compression, and processing operations. Quantum Inform. Process. 10(1), 63–84 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Tseng, C.-C., Hwang, T.-M.: Quantum digital image processing algorithms. 16th IPPR Conference on Computer Vision, Graphics and Image Processing, pp. 827–834 (2003)

  11. Xiaowei Fu, Ding, Mingyue: A new quantum edge detection algorithm for medical images. Proceeding of Medical Imaging, Parallel Processing of Images and Optimization Techniques, SPIE vol. 7497 (2009)

  12. Le, P.Q., Iliyasu, A.M., Dong, F., Hirota, K.: Strategies for designing geometric transformations on quantum images. Theor. Comput. Sci. 412, 1406–1418 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Le, P.Q., Iliyasu, A.M., Dong, F., Hirota, K.: Efficient color transformations on quantum images. J. Adv. Comput. Intell. Intell. Inform. 15(6), (2011)

  14. Sun, B., Le, P.Q., Iliyasu, A.M.: A multi-channel representation for images on quantum computers using the RGB\(\alpha \) color Space. Proceedings of the IEEE 7th International Symposium on Intelligent, Signal Processing, pp. 160–165 (2011)

  15. Iliyasu, A.M., Le, P.Q., Dong, F., Hirota, K.: Watermarking and authentication of quantum images based on restricted geometric transformations. Inform. Sci. 186, 126–149 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  16. Zhang, W., Gao, F., Liu, B., Wen, Q., Chen, H.: A watermark strategy for quantum images based on quantum fourier transform. Quantum Inform. Process. doi:10.1007/s11128-012-0423-6 (2012)

  17. Yang, G.W., Song, X.Y., Hung, W.N.N., et al.: Group theory based synthesis of binary reversible circuits. Lecture Notes Comput. Sci. 3959, 365–374 (2006)

    Article  MathSciNet  Google Scholar 

  18. Lloyd, S.: Almost any quantum logic gate is universal. Phys. Rev. Lett. 75(2), 346–349 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  19. Brayton, R.K., Sangiovanni-Vincentelli, A., McMullen, C., Hachtel, G.: Log. Minimization Algorithms VLSI Synth. Kluwer Academic Publishers, Dordrecht (1984)

    Book  Google Scholar 

  20. Pang, C., Zhou, Z., Guo, G.: A hybrid quantum encoding algorithm of vector quantization for image compression. Chin. Phys. arXiv:cs/0605002 (2006)

  21. Durr, C., Hoyer, P.: A quantum algorithm for finding the minimum. arXiv:quant-ph/9607014 (1996)

Download references

Acknowledgments

The authors appreciate the kind comments and professional criticisms of the anonymous reviewer. This has greatly enhanced the overall quality of the manuscript and opened numerous perspectives geared toward improving the work. This work is supported in part by the National High-tech R&D Program of China (863 Program) under Grants 2012AA01A301 and 2012AA010901. And it is partially supported by National Science Foundation (NSF) China 61103082 and 61170261. Moreover, it is a part of Innovation Fund Sponsor Project of Excellent Postgraduate Student (B120601 and CX2012A002).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yi Zhang.

Additional information

This work is supported in part by the National High-tech R&D Program of China (863 Program) under Grants 2012AA01A301 and 2012AA010901. And it is partially supported by National Science Foundation (NSF) China 61103082 and 61170261. Moreover, it is a part of Innovation Fund Sponsor Project of Excellent Postgraduate Student (B120601 and CX2012A002).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, Y., Lu, K., Gao, Y. et al. NEQR: a novel enhanced quantum representation of digital images. Quantum Inf Process 12, 2833–2860 (2013). https://doi.org/10.1007/s11128-013-0567-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-013-0567-z

Keywords

Navigation