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Image Representation and Processing Using Ternary Quantum Computing

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Adaptive and Natural Computing Algorithms (ICANNGA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7824))

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Abstract

In this paper we address the recently outlined field of Quantum Image Processing and propose a novel model for representing a quantum image. In our approach we use multilevel quantum systems to store and process images because of their advantages in terms of dimension of the available Hilbert space, computational power, physical implementation and security of quantum cryptographic protocols. In particular, we focus on the quantum image representation using qutrits (3-level quantum systems) and discuss possible implementations for basic image processing tasks such as image complement, image binarization and histogram computation.

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References

  1. Shor, P.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proc. of the 35th Annual Symp. on Foundations of Computer Science, pp. 124–134. IEEE Computer Society (1994)

    Google Scholar 

  2. Grover, L.: A fast quantum mechanical algorithm for database search. In: Proc. of 28th ACM Annual STOC, pp. 212–219 (1996)

    Google Scholar 

  3. Venegas-Andraca, S., Ball, J.: Storing images in engtangled quantum systems. arXiv:quant-ph/0402085 (2003)

    Google Scholar 

  4. Venegas-Andraca, S., Bose, S.: Storing, processing and retrieving an image using quantum mechanics. In: Proc. of the SPIE Conf. Quantum Information and Computation, pp. 137–147 (2003)

    Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  8. Fijany, A., Williams, C.: Quantum wavelet transform: fast algorithm and complete circuits. arXiv:quant-ph/9809004 (1998)

    Google Scholar 

  9. Klappenecker, A., Roetteler, M.: Discrete cosine transforms on quantum computers. In: IEEER8-EURASIP Symp. on Image and Signal Processing and Analysis (ISPA 2001), Pula, Croatia, pp. 464–468 (2001)

    Google Scholar 

  10. Lomont, C.: Quantum convolution and quantum correlation algorithms are physically impossible. arXiv:quant-ph/0309070 (2003)

    Google Scholar 

  11. Bruß, D., Macchiavello, C.: Optimal eavesdropping in cryptography with three-dimensional quantum states. Phys. Rev. Lett. 88, 127901 (2002)

    Article  Google Scholar 

  12. Durt, T., Cerf, N.J., Gisin, N., Żukowski, M.: Security of quantum key distribution with entangled qutrits. Phys. Rev. A 67, 012311 (2003)

    Google Scholar 

  13. Spekkens, R.W., Rudolph, T.: Degrees of concealment and bindingness in quantum bit commitment protocols. Phys. Rev. A 65, 012310 (2001)

    Google Scholar 

  14. Greentree, A.D., Schirmer, S.G., Green, F., Hollenberg, L.C.L., Hamilton, A.R., Clark, R.G.: Maximizing the hilbert space for a finite number of distinguishable quantum states. Phys. Rev. Lett. 92, 097901 (2004)

    Article  Google Scholar 

  15. Ralph, T.C., Resch, K.J., Gilchrist, A.: Efficient toffoli gates using qudits. Phys. Rev. A 75, 022313 (2007)

    Google Scholar 

  16. Lanyon, B., Barbieri, M., Almeida, M., Jennewein, T., Ralph, T., Resch, K., Pryde, G., O’Brien, J., Gilchrist, A., White, A.: Simplifying quantum logic using higher-dimensional hilbert spaces. Nature Physics 5(2), 134–140 (2008)

    Article  Google Scholar 

  17. Collins, D., Gisin, N., Linden, N., Massar, S., Popescu, S.: Bell inequalities for arbitrarily high-dimensional systems. Phys. Rev. Lett. 88, 040404 (2002)

    Article  MathSciNet  Google Scholar 

  18. Acin, A., Durt, T., Gisin, N., Latorre, J.I.: Quantum nonlocality in two three-level systems. Phys. Rev. A 65, 052325 (2002)

    Google Scholar 

  19. Vallone, G., Pomarico, E., De Martini, F., Mataloni, P., Barbieri, M.: Experimental realization of polarization qutrits from nonmaximally entangled states. Phys. Rev. A 76, 012319 (2007)

    Article  Google Scholar 

  20. Neeley, M., Ansmann, M., Bialczak, R.C., Hofheinz, M., Lucero, E., O’Connell, A.D., Sank, D., Wang, H., Wenner, J., Cleland, A.N., Geller, M.R., Martinis, J.M.: Emulation of a Quantum Spin with a Superconducting Phase Qudit. Science 325, 722 (2009)

    Article  Google Scholar 

  21. Straupe, S., Kulik, S.: Quantum optics: The quest for higher dimensionality. Nature Photonics 4, 585–586 (2010)

    Article  Google Scholar 

  22. Bianchetti, R., Filipp, S., Baur, M., Fink, J.M., Lang, C., Steffen, L., Boissonneault, M., Blais, A., Wallraff, A.: Control and tomography of a three level superconducting artificial atom. Phys. Rev. Lett. 105, 223601 (2010)

    Article  Google Scholar 

  23. Muthukrishnan, A., Stroud, C.R.: Multivalued logic gates for quantum computation. Phys. Rev. A 62(5), 052309 (2000)

    Article  MathSciNet  Google Scholar 

  24. Perkowski, M., Al-Rabadi, A., Kerntopf, P.: Multiple-valued quantum logic synthesis. In: Proc. of Intl. Symp. on New Paradigm VLSI Computing, Sendai, Japan, December 12-14, pp. 41–47 (2002)

    Google Scholar 

  25. Miller, D., Maslov, D., Dueck, G.: Synthesis of quantum multiple-valued circuits. J. Multiple-Valued Logic Soft Comput. 12(5-6), 431–450 (2006)

    MathSciNet  MATH  Google Scholar 

  26. Khan, M., Perkowski, M.: Genetic algorithm based synthesis of multi-output ternary functions using quantum cascade of generalized ternary gates. In: Congress on Evolutionary Computation, vol. 2, pp. 2194–2201 (2004)

    Google Scholar 

  27. Mohammadi, M., Niknafs, A., Eshghi, M.: Controlled gates for multi-level quantum computation. Quantum Inf. Process. 10(2), 241–256 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  28. Yang, G., Song, X., Perkowski, M.A., Wu, J.: Realizing ternary quantum switching networks without ancilla bits. Journal of Physics A: Mathematical and General 38(44), 9689–9697 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  29. Mandal, S., Chakrabarti, A., Sur-Kolay, S.: Synthesis techniques for ternary quantum logic. In: 41st IEEE Intl. Symp. on Multiple-Valued Logic, pp. 218–223 (2011)

    Google Scholar 

  30. Giesecke, N., Kim, D.H., Hossain, S., Perkowski, M.: Search for universal ternary quantum gate sets with exact minimum costs. In: Proc. of RM Symp., Oslo, May 16 (2007)

    Google Scholar 

  31. Zadeh, R.P., Haghparast, M.: A new reversible/quantum ternary comparator. Australian Journal of Basic and Applied Sciences 5(12), 2348–2355 (2011)

    Google Scholar 

  32. Khan, M.H.A.: Design of reversible/quantum ternary comparator circuits. Engineering Letters 16(2), 178–184 (2008)

    Google Scholar 

  33. Brassard, G., Hoyer, P., Tapp, A.: Quantum counting, arXiv:quant-ph/9805082v1 (1998)

    Google Scholar 

  34. Williams, C.: Explorations in Quantum Computing, 2nd edn. Springer (2011)

    Google Scholar 

  35. Klimov, A.B., Guzmán, R., Retamal, J.C., Saavedra, C.: Qutrit quantum computer with trapped ions. Phys. Rev. A 67, 62313 (2003)

    Article  Google Scholar 

  36. Zilic, Z., Radecka, K.: Scaling and better approximating quantum fourier transform by higher radices. IEEE Trans. Comput. 56(2), 202–207 (2007)

    Article  MathSciNet  Google Scholar 

  37. Fan, Y.: Applications of multi-valued quantum algorithms (2007), http://arxiv.org/pdf/0809.0932

  38. Li, H., Wu, C., Liu, W., Chen, P., Li, C.: Fast quantum search algorithm for databases of arbitrary size and its implementation in a cavity qed system. Phys. Lett. A 375(48), 4249–4254 (2011)

    Article  MATH  Google Scholar 

  39. Parasa, V., Perkowski, M.: Quantum phase estimation using multivalued logic. In: IEEE Intl. Symp. on Multiple-Valued Logic, pp. 224–229 (2011)

    Google Scholar 

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Caraiman, S., Manta, V. (2013). Image Representation and Processing Using Ternary Quantum Computing. In: Tomassini, M., Antonioni, A., Daolio, F., Buesser, P. (eds) Adaptive and Natural Computing Algorithms. ICANNGA 2013. Lecture Notes in Computer Science, vol 7824. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37213-1_38

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  • DOI: https://doi.org/10.1007/978-3-642-37213-1_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37212-4

  • Online ISBN: 978-3-642-37213-1

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