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Asymmetric scaling of a quantum image based on bilinear interpolation with arbitrary scaling ratio

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Abstract

As a branch of quantum image processing, the quantum image scaling has been widely studied in the recent years. In this paper, an asymmetric scaling for quantum image with arbitrary scaling ratio is proposed. Firstly, the generalized quantum image representation is employed to represent a quantum image of arbitrary size \(H \times W\), and the bilinear interpolation is utilized to obtain the interpolated image. Then, the quantum circuit of the quantum image scaling algorithm with different scaling ratios in two dimensions is designed. Finally, the network complexity and simulation results of the two scaling methods are analyzed. The final result shows that the proposed scheme is a quadratic function, which is much lower than the cubic function and exponential function of other bilinear interpolation schemes.

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References

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

    Article  MathSciNet  Google Scholar 

  2. Deutsch, D.: Quantum theory, the Church–Turing principle and the universal quantum computer. In: Proceedings of the royal society of London. A. mathematical and physical sciences 400.1818, 97–117 (1985)

  3. 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)

  4. 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)

  5. Vlasov, A.Y.: Quantum computations and images recognition. arXiv:quant-ph/9703010. (1997)

  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. 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 

  8. 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 

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

    Article  ADS  MathSciNet  Google Scholar 

  10. Jiang, N., Luo, W.: Quantum image scaling using nearest neighbor interpolation. Quantum Inf. Process. 14(1559), 1571 (2015)

    MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  13. Li, P., Liu, X.: Bilinear interpolation method for quantum images based on quantum Fourier transform. Int. J. Quantum Inf. 16, 1850031 (2018)

    Article  MathSciNet  Google Scholar 

  14. Zhou, R.-G., Cheng, Y., Liu, D.: Quantum image scaling based on bilinear interpolation with arbitrary scaling ratio. Quantum Inf. Process. 18(9), 267 (2019)

    Article  ADS  Google Scholar 

  15. Zhou, R.G., Cheng, Y., Qi, X., et al.: Asymmetric scaling scheme over the two dimensions of a quantum image. Quantum Inf Process 19, 343 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  16. Yan, F., et al.: Implementing bilinear interpolation with quantum images. Digital Signal Process. 117, 103149 (2021)

    Article  Google Scholar 

  17. Le, P.Q., Iliyasu, A.M., Dong, F., Hirota, K.: Fast geometric transformations on quantum images. IAENG Int. J. Appl. Math. 40, 3 (2010)

    MathSciNet  MATH  Google Scholar 

  18. Le, P.Q., et al.: Efficient color transformations on quantum images. J. Adv. Comput. Intell. Intell. Inf. 15, 698–706 (2011)

    Article  Google Scholar 

  19. Zhang, Y., et al.: Local feature point extraction for quantum images. Quantum Inf. Process. 14, 1573–1588 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  20. Caraiman, S., Vasile, I.M.: Image segmentation on a quantum computer. Quantum Inf. Process. 14, 1693–1715 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  21. Zhou, R.G., Hu, W., Fan, P.: Quantum watermarking scheme through Arnold scrambling and LSB steganography. Quantum Inf. Process. 16, 1–21 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  22. Gonzalez, R.C., Woods, R.E.: Digital image processing. Prentice Hall, New Jersey (2007)

    Google Scholar 

  23. 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  Google Scholar 

  24. 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)

  25. 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)

  26. Khosropour, A., Aghababa, H., Forouzandeh, B.: Quantum division circuit based on restoring division algorithm. In: Eighth International Conference on Information Technology: New Generations, Itng 2011, Las Vegas, 11–13 April, DBLP, pp. 1037–1040 (2011)

  27. Thapliyal, H., et al.: Quantum circuit designs of integer division optimizing T-count and T-depth. IEEE Trans. Emerg. Topics Comput. 9, 1045 (2019)

    Article  Google Scholar 

  28. Muñoz-Coreas, E., Himanshu, T.: Quantum circuit design of a t-count optimized integer multiplier. IEEE Trans. Comput. 68, 729–739 (2018)

    Article  MathSciNet  Google Scholar 

  29. 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)

  30. 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 

  31. Ruiz-Perez, L., Garcia-Escartin, J.C.: Quantum arithmetic with the quantum Fourier transform. Quantum Inf. Process. 16(6), 152 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  32. Nielson, M.A., Chuang, I.L.: Quantum computation and quantum information. Cambridge University Press, Cambridge (2000)

    Google Scholar 

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 6217070290, Shanghai Science and Technology Project under Grant No. 21JC1402800 and 20040501500, and Top-notch Innovative Talent Program for Postgraduate Students of Shanghai Maritime University under Grant No. 2021YBR009.

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Correspondence to Ri-Gui Zhou.

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Gao, C., Zhou, RG., Li, X. et al. Asymmetric scaling of a quantum image based on bilinear interpolation with arbitrary scaling ratio. Quantum Inf Process 21, 270 (2022). https://doi.org/10.1007/s11128-022-03612-8

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