Skip to main content
SpringerLink
Log in

Quantum Image Scaling Based on Bilinear Interpolation with Decimals Scaling Ratio

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

Quantum image scaling is an important branch of quantum image processing and has been extensively studied in recent years. A quantum image scaling algorithm based on bilinear interpolation is proposed in this paper. This algorithm can scale the image of any floating point number scale. Quantum arithmetics for floating point numbers are proposed, and quantum algorithms for quantum image scaling up and down are presented. Moreover, the quantum circuits of quantum image scaling are designed and their network complexity is analyzed. With the results of simulation experiment on the classical computer MATLAB software, it is demonstrated that the proposed quantum image scaling algorithms have the good effect.

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

Access this article

Log in via an institution

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
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28

Similar content being viewed by others

References

  1. Feynman, R.P.: Simulating physics with computers. Int. J. Theor. Phys. 21(6/7), 467–488 (1982)

    Article  MathSciNet  Google Scholar 

  2. Shor, P.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 124–134 (1994)

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

  4. Li, Y.C., Zhou, R., Xu, R.Q., Luo, J., Jiang, S.-X.: A Quantum Mechanics-Based Framework for EEG Signal Feature Extraction and Classification. IEEE Trans. Emerg. Top. Comput. (2020). doi:https://doi.org/10.1109/tetc.2020.3000734

  5. Li, Y.C., Zhou, R.-G., Xu, R.Q., Luo, J., Hu, W.W.: A Quantum Deep Convolutional Neural Network for Image Recognition. Quantum Sci. Technol. 5(4), 044003 (2020). https://doi.org/10.1088/2058-9565/ab9f93

    Article  ADS  Google Scholar 

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

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

  8. Venegas-Andraca, S.E., Ball, J.L.: Processing images in entangled quantum systems. Quantum Inf.Process. 9(1), 1–11 (2010)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  10. Zhang, Y., Lu, K., Gao, Y.H., Wang, M.: NEQR: a novel enhanced quantum representation of digital images. Quantum Inf. Process. 12(12), 2833–2860 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  11. Jiang, N., Wang, L.: Quantum image scaling using nearest neighbor interpolation. Quantum Inf. Process. 14(5), 1559–1571 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  12. Jiang, N., Wang, J., Mu, Y.: Quantum image scaling up based on nearest-neighbor interpolation with integer scaling ratio. Quantum Inf. Process. 14(11), 4001–4026 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  13. Zhang, Y., Lu, K., Gao, Y.H., Xu, K.: A novel quantum representation for log-polar images. Quantum Inf. Process. 12(2), 3103–3126 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  14. Li, H.S., Zhu, Q.X., Lan, S., Shen, C.Y., Zhou, R.G., Mo, J.: Image storage, retrieval, compression and segmentation in a quantum system. Quantum Inf. Process. 12(6), 2269–2290 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  15. Li, H.S., Zhu, Q.X., Zhou, R.G., Lan, S., Yang, X.J.: Multi-dimensional color image storage and retrieval for a normal arbitrary quantum superposition state. Quantum Inf. Process. 13(4), 991–1011 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  16. Le, P.Q., Iliyasu, A.M., Dong, F.Y., Hirota, K.: Fast geometric transformation on quantum images. IAENG Int. J. Appl. Math. 40(3), 113–123 (2010)

    MathSciNet  MATH  Google Scholar 

  17. Wang, J., Jiang, N., Wang, L.: Quantum image translation. Quantum Inf. Process. 14(5), 1589–1604 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  18. Gonzalez, R., Woods, R.: Digital Image Processing, 3rd edn. Prentice Hall, New Jersey (2007)

    Google Scholar 

  19. http://www.mathworks.cn/cn/help/images/ref/imresize.html (2014)

  20. Nachtigal, M., Thapliyal, H., Ranganathan, N.: Design of a reversible floating-point adder architecture, In 2011 11th IEEE International Conference on Nanotechnology. IEEE, pp. 451–456 (2011)

  21. Nguyen, T.D., Van Meter, R.: A resource-efficient design for a reversible floating point adder in quantum computing. ACM J. Emerg. Technol. Comput. Syst. (JETC). 11(2), 13 (2014)

    Google Scholar 

  22. Haener, T., Soeken, M., Roetteler, M., Svore, K.M.: Quantum circuits for floating-point arithmetic, In International Conference on Reversible Computation. Springer, pp. 162–174 (2018)

  23. Sang, J.Z., Wang, S., Niu, X.M.: Quantum realization of the nearest-neighbor interpolation method for FRQI and NEQR. Quantum Inf. Process. 15(1), 37–64 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  24. Zhou, R.G., Hu, W.W., Fan, P., Ian, H.: Quantum realization of the bilinear interpolation method for NEQR. Sci. Rep. 7, 2511 (2017)

    Article  ADS  Google Scholar 

  25. Zhou, R.G., Liu, X., Luo, J.: Quantum circuit realization of the bilinear interpolation method for GQIR. Int. J. Theor. Phys. 56(9), 2966–2980 (2017)

    Article  MathSciNet  Google Scholar 

  26. Li, H.S., Fan, P., Xia, H.Y., et al.: Quantum Implementation Circuits of Quantum Signal Representation and Type Conversion[J]. IEEE Trans. Circuits Syst. Regul. Pap. PP(1), 1–14 (2018)

    Article  Google Scholar 

  27. Islam, M.S., Rahman, M.M., Begum, Z., Hafiz, M.Z.: Low cost quantum realization of reversible multiplier circuit. Inf. Technol. J. 8(2), 208–213 (2009)

    Article  Google Scholar 

  28. Thapliyal, H., Ranganathan, N.: Design of efficient reversible binary subtractors based on a new reversible gate. In: Proceedings of the IEEE Computer Society Annual Symposium on VLSI, Tampa, pp. 229–234 (2009)

  29. Thapliyal, H., Ranganathan, N.: A new design of the reversible subtractor circuit. In: 2011 11th IEEE conference on nanotechnology (IEEE-NANO), IEEE, pp. 1430–1435 (2011)

  30. Shuofei, T.: Principles of Computer Composition[M]. Higher Education Press. (in Chinese) (2002)

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

    Google Scholar 

  32. Zhou, R.G., Hu, W.W., Luo, G.F., Liu, X.A., Fan, P.: Quantum realization of the nearest neighbor value interpolation method for INEQR[J]. Quantum Inf. Process. 17(7), 166 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  33. Zhou R G , Cheng Y, Liu D Q.: Quantum image scaling based on bilinear interpolation with arbitrary scaling ratio[J]. Quantum Inf. Process, 18(9) (2019)

  34. Bacon, J.W.: Computer science 315 lecture notes, (2010)

  35. Draper, T.G.: Addition on a quantum computer, arXiv preprint quantph/0008033, (2000)

  36. Ruiz-Perez, L., Garcia-Escartin, J.C.: Quantum arithmetic with the quantum fourier transform. Quantum Inf. ProcessS. 16(6), 152–166 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  37. Vedral, V., Barenco, A., Ekert, A.: Quantum networks for elementary arithmetic operations. Phys. Rev. A. 54(1), 147–153 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  38. Cheng, K.-W., Tseng, C.-C.: Quantum full adder and subtractor. Electron. Lett. 38(22), 1343–1344 (2002)

    Article  ADS  Google Scholar 

  39. Fahdil, M.A.: Operations algorithms on quantum computer, J. Comput.Sci., vol. 10, no. 1, (2010)

  40. Ratnaparkhi, P.P., Bikash, K.: Demonstration of a quantum calculator on ibm quantum experience platform DOI:https://doi.org/10.13140/RG.2.2.12661.63209

  41. Thapliyal, H., Ranganathan, N.: Design of efficient reversible binary subtractors based on a new reversible gate, In 2009 IEEE computer society Annual symposium on VLSI. IEEE, pp. 229–234 (2009)

  42. Thapliyal, H., Ranganathan, N.: A New Design of the Reversible Subtractor Circuit[C]// 2011 11th IEEE International Conference on Nanotechnology. IEEE, (2012)

  43. Thapliyal, H., Srinivas, M.: Novel reversible multiplier architecture using reversible tsg gate, arXiv preprint cs/0605004, (2006)

  44. Islam, M.S., Rahman, M., Begum, Z., Hafiz, M.Z.: Low cost quantum realization of reversible multiplier circuit. Inf. Technol. J. 8(2), 208–213 (2009)

    Article  Google Scholar 

  45. Kotiyal, S., Thapliyal, H., Ranganathan, N.: Circuit for reversible quantum multiplier based on binary tree optimizing ancilla and garbage bits, In 2014 27th International Conference on VLSI Design and 2014 13th International Conference on Embedded Systems. IEEE, pp.545–550 (2014)

  46. Thapliyal, H., Munoz-Coreas, E., Varun, T., Humble, T.: Quantum Circuit Designs of Integer Division Optimizing T-Count and T-Depth, IEEE Transactions on Emerging Topics in Computing, (2019)

  47. Khosropour, A., Aghababa, H., Forouzandeh, B.: Quantum division circuit based on restoring division algorithm, In 2011 Eighth International Conference on Information Technology: New Generations. IEEE, pp. 1037–1040 (2011)

Download references

Acknowledgements

This work is supported by the Shanghai Science and Technology Project in 2020 under Grant No.20040501500.

Author information

Authors and Affiliations

  1. College of Information Engineering, Shanghai Maritime University, Shanghai, 201306, China

    Ri-Gui Zhou & Chuan Wan

  2. Research Center of Intelligent Information Processing and Quantum Intelligent Computing, Shanghai, 201306, China

    Ri-Gui Zhou & Chuan Wan

Authors
  1. Ri-Gui Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chuan Wan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chuan Wan.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhou, RG., Wan, C. Quantum Image Scaling Based on Bilinear Interpolation with Decimals Scaling Ratio. Int J Theor Phys 60, 2115–2144 (2021). https://doi.org/10.1007/s10773-021-04829-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-021-04829-6

Keywords

Search

Navigation