Efficient Color Transformations on Quantum Images
Phuc Q. Le, Abdullah M. Iliyasu, Fangyan Dong,
and Kaoru Hirota
Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, G3-49, 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan
Efficient transformations on the color content of images using single qubit operations are proposed based on the Flexible Representation of Quantum Images (FRQI). Utilizing the single qubit dedicated for encoding color information in the FRQI representation, the proposed operations offer massive speed-up in terms of changes in the color information in comparison with classical ones. Simulations of the FRQI images and circuits of these transformations using synthetic and Lena images on classical computers demonstrate the feasibility of the proposal. Together with position related operations, the color transformations could provide the foundation to achieve practical applications which are inefficient at present.
-  R. P. Feynman, “Simulating physics with computers,” Int. J. of Theoretical Physics, Vol.21, No.6-7, pp. 467-488, 1982.
-  L. Grover, “A fast quantum mechanical algorithm for database search,” Proc. of the 28th Ann. ACM Symp. on the Theory of Computing (STOC 1996), pp. 212-219, 1996.
-  P. W. Shor, “Algorithms for quantum computation: discrete logarithms and factoring,” Proc. 35th Ann. Symp. Foundations of Computer Science, IEEE Computer Soc. Press, Los Almitos, CA. pp. 124-134, 1994.
-  M. Nielsen and I. Chuang, “Quantum computation and quantum information,” Cambridge University Press, New York, 2000.
-  A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. W. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. Part A, Vol.52, p. 3457, 1995.
-  T. Monz, K. Kim, W. Hansel, M. Riebe, A. S. Villar, P. Schindler, M. Chwalla, M. Hennrich, and R. Blatt, “Realization of the quantum Toffoli gate with trapped ions,” Phys. Rev. Let., Vol.102, 040501, 2009.
-  G. Beach, C. Lomont, and C. Cohen, “Quantum image processing(quip),” Proc. of Applied Imagery Pattern Recognition Workshop, pp. 39-44, 2003.
-  S. Caraiman and V. I. Manta, “New applications of quantum algorithms to computer graphics: the quantum random sample consensus algorithm,” Proc. of the 6th ACM Conf. on Computing frontier, pp. 81-88, 2009.
-  D. Curtis and D. A. Meyer, “Towards quantum template matching,” Proc. of the SPIE, Vol.5161. pp. 134-141, 2004.
-  A. Fijany and C. P. Williams, “Quantum wavelet transform: fast algorithm and complete circuits,” 1998.
-  A. Klappenecker and M. Röotteler, “Discrete cosine transforms on quantum computers,” Proc. of the 2nd Int. Symp. on Image and Signal Processing and Analysis, pp. 464-468, 2001.
-  C. C. Tseng and T. M. Hwang, “Quantum circuit design of 8×8 discrete cosine transforms using its fast computation on graph,” ISCAS 2005, Vol.1, pp. 828-831, 2005.
-  P. Q. Le, F. Dong, and K. Hirota, “A flexible representation of quantum images for polynomial preparation, image compression, and processing operations,” Quantum Information Processing, 2010.
-  S. E. Venegas-Andraca and J. L. Ball, “Processing images in entangled quantum systems,” Quantum Information Processing, Vol.9, No.1, pp. 1-11, 2010.
-  S. E. Venegas-Andraca and S. Bose, “Storing, processing and retrieving an image using quantum mechanics,” Proc. of the SPIE Conf. Quantum Information and Computation, pp. 137-147, 2003.
-  J. I. Latorre, “Image compression and entanglement,” 2005.
-  C. Lomont, “Quantum convolution and quantum correlation algorithms are physically impossible,” 2003.
-  P. Q. Le, A. M. Iliyasu, F. Dong, and K. Hirota, “Fast geometric transformations on quantum images,” IAENG Int. J. of Applied Mathematics, Vol.40, No.3, pp. 113-123, 2010.
-  A. M. Iliyasu, P. Q. Le, F. Dong, and K. Hirota, “Restricted geometric transformations and their applications for quantum image watermarking and authentication,” in: Proc. of Asian Conf. on Quantum Information Science, pp. 96-97, 2010.
-  P. Q. Le, A. M. Iliyasu, F. Dong, and K. Hirota, “Strategies for designing geometric transformations on quantum images,” Theoretical Computer Science, 2010.