Abstract
A flexible representation for quantum images (FRQI) is proposed to provide a representation for images on quantum computers which captures information about colors and their corresponding positions in the images. A constructive polynomial preparation for the FRQI state from an initial state, an algorithm for quantum image compression (QIC), and invertible processing operations for quantum images are combined to build the whole process for quantum image processing based on FRQI. The simulation experiments on FRQI include storage and retrieval of images and detecting a line from binary images by applying quantum Fourier transform as a processing operation. The compression ratios of QIC between groups of same color positions range from 68.75% to 90.63% on single digit images and 6.67% to 31.62% on the Lena image. The FRQI provides a foundation not only to express images but also to explore theoretical and practical aspects of image processing on quantum computers.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., Sleator, T., Smolin, J.A., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. A 52, 3457 (1995)
Beach, G., Lomont, C., Cohen, C.: Quantum image processing (quip). In: Proc. of Applied Imagery Pattern Recognition Workshop, pp. 39–44 (2003)
Brayton, R.K., Sangiovanni-Vincentelli, A., McMullen, C., Hachtel, G.: Logic minimization algorithms for VLSI synthesis. Kluwer Academic Publishers, Dordrecht (1984)
Caraiman, S., Manta, V.I.: New applications of quantum algorithms to computer graphics: the quantum random sample consensus algorithm. In: Proc. of the 6th ACM Conference on Computing Frontier, pp. 81–88 (2009)
Curtis, D., Meyer, D.A.: Towards quantum template matching. In: Proc. of the SPIE, vol. 5161, pp. 134–141 (2004)
Feynman, R.P.: Simulating physics with computers. International Journal of Theoretical Physics 21(6/7), 467–488 (1982)
Fijany, A., Williams, C. P.: Quantum wavelet transform: fast algorithm and complete circuits. arXiv:quant-ph/9809004 (1998)
Grover, L.: A fast quantum mechanical algorithm for database search. In: Proc. of the 28th Ann. ACM Symp. on the Theory of Computing (STOC 1996), pp. 212–219 (1996)
Klappenecker, A., Rötteler, M.: Discrete cosine transforms on quantum computers. In: Proc. of the 2nd Inter. Symp. on Image and Signal Processing and Analysis, pp. 464–468 (2001)
Latorre, J. I.: Image compression and entanglement. arXiv:quant-ph/0510031 (2005)
Lomont, C.: Quantum convolution and quantum correlation algorithms are physically impossible. arXiv:quant-ph/0309070 (2003)
Lomont, C.: Quantum circuit identities. arXiv:quant-ph/0307111 (2003)
Maslov, D., Dueck, G.W., Miller, D.M., Camille, N.: Quantum circuit simplification and level compaction. IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems 27(3), 436–444 (2008)
Nielsen, M., Chuang, I.: Quantum computation and quantum information. Cambridge University Press, New York (2000)
Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proc. 35th Ann. Symp. Foundations of Computer Science, pp. 124–134. IEEE Computer Soc. Press, Los Almitos (1994)
Tseng, C.C., Hwang, T.M.: Quantum circuit design of 8×8 discrete cosine transforms using its fast computation flow graph. In: ISCAS 2005, vol. I, pp. 828–831 (2005)
Venegas-Andraca, S. E., Ball, J. L.: Storing Images in engtangled quantum systems. arXiv:quant-ph/0402085 (2003)
Venegas-Andraca, S.E., 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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Le, P.Q., Iliyasu, A.M., Dong, F., Hirota, K. (2011). A Flexible Representation and Invertible Transformations for Images on Quantum Computers. In: Ruano, A.E., Várkonyi-Kóczy, A.R. (eds) New Advances in Intelligent Signal Processing. Studies in Computational Intelligence, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11739-8_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-11739-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11738-1
Online ISBN: 978-3-642-11739-8
eBook Packages: EngineeringEngineering (R0)