{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,10]],"date-time":"2026-05-10T14:41:04Z","timestamp":1778424064779,"version":"3.51.4"},"reference-count":62,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2014,10,10]],"date-time":"2014-10-10T00:00:00Z","timestamp":1412899200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A flexible representation of quantum images (FRQI) was proposed to facilitate the extension of classical (non-quantum)-like image processing applications to the quantum computing domain. The representation encodes a quantum image in the form of a normalized state, which captures information about colors and their corresponding positions in the images. Since its conception, a handful of processing transformations have been formulated, among which are the geometric transformations on quantum images (GTQI) and the CTQI that are focused on the color information of the images. In addition, extensions and applications of FRQI representation, such as multi-channel representation for quantum images (MCQI), quantum image data searching, watermarking strategies for quantum images, a framework to produce movies on quantum computers and a blueprint for quantum video encryption and decryption have also been suggested. These proposals extend classical-like image and video processing applications to the quantum computing domain and offer a significant speed-up with low computational resources in comparison to performing the same tasks on traditional computing devices. Each of the algorithms and the mathematical foundations for their execution were simulated using classical computing resources, and their results were analyzed alongside other classical computing equivalents. The work presented in this review is intended to serve as the epitome of advances made in FRQI quantum image processing over the past five years and to simulate further interest geared towards the realization of some secure and efficient image and video processing applications on quantum computers.<\/jats:p>","DOI":"10.3390\/e16105290","type":"journal-article","created":{"date-parts":[[2014,10,10]],"date-time":"2014-10-10T10:24:07Z","timestamp":1412936647000},"page":"5290-5338","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":53,"title":["Quantum Computation-Based Image Representation, Processing Operations and Their Applications"],"prefix":"10.3390","volume":"16","author":[{"given":"Fei","family":"Yan","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Changchun University of Science and Technology, No. 7089, Weixing Road, Changchun 130022, China"},{"name":"Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, G3-49, 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdullah","family":"Iliyasu","sequence":"additional","affiliation":[{"name":"Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, G3-49, 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan"},{"name":"College of Engineering, Salman Bin Abdulaziz University, P.O. Box 173, Al-Kharj 11942, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengang","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Changchun University of Science and Technology, No. 7089, Weixing Road, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,10,10]]},"reference":[{"key":"ref_1","unstructured":"Yan, F. (2014). Quantum Computation Based Image Data Searching, Image Watermarking, and Representation of Emotion Space. [Ph.D. Thesis, Tokyo Institute of Technology]."},{"key":"ref_2","unstructured":"Iliyasu, A. (2012). Algorithmic Frameworks to Support the Realisation of Secure and Efficient Image-Video Processing Applications on Quantum Computers. [Ph.D. Thesis, Tokyo Institute of Technology]."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1007\/BF02650179","article-title":"Simulating physics with computers","volume":"21","author":"Feynman","year":"1982","journal-title":"Int. J. Theor. Phys"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1098\/rspa.1985.0070","article-title":"Quantum theory, the church-turing principle and the universal quantum computer","volume":"400","author":"Deutsch","year":"1985","journal-title":"Proc. R. Soc. Lond. A"},{"key":"ref_5","unstructured":"Shor, P. (1994, January 20\u201322). Algorithms for Quantum Computation: Discrete Logarithms and Factoring. Santa Fe, NM, USA."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1221","DOI":"10.1126\/science.1173731","article-title":"Shor\u2019s quantum factoring algorithm on a photonic chip","volume":"325","author":"Politi","year":"2009","journal-title":"Science"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Grover, L. (1996, January 22\u201324). A fast quantum mechanical algorithm for database search. Philadelphia, PA, USA.","DOI":"10.1145\/237814.237866"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1103\/PhysRevA.68.042328","article-title":"Experimental requirements for grover\u2019s algorithm in optical computing","volume":"68","author":"Dodd","year":"2003","journal-title":"Phys. Rev. A"},{"key":"ref_9","unstructured":"Chow, J.M., Corcoles, A.D., Gambetta, J.M., Rigetti, C., Johnson, B., Smolin, J., Merkel, S., Poletto, S., Rozen, J., and Rothwell, M.B. (March, January 27). High-fidelity gates towards a scalable super-conducting quantum processor. Boston, MA, USA."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1007\/3-540-44678-8_4","article-title":"Quantum algorithms: Applicable algebra and quantum physics","volume":"173","author":"Beth","year":"2001","journal-title":"Springer Tracts Mod. Phys"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2563","DOI":"10.1016\/j.nimb.2009.05.061","article-title":"Critical issues in the formation of quantum computer test structures by ion implantation","volume":"267","author":"Schenkel","year":"2009","journal-title":"Nucl. Instrum. Methods Phys. Res. Sect. B"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1459","DOI":"10.1142\/S0219749911008015","article-title":"A framework for representing and producing movies on quantum computers","volume":"9","author":"Iliyasu","year":"2011","journal-title":"Int. J. Quantum Inf"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.tcs.2004.03.041","article-title":"Quantum computing without entanglement","volume":"320","author":"Biham","year":"2004","journal-title":"Theor. Comput. Sci"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3457","DOI":"10.1103\/PhysRevA.52.3457","article-title":"Elementary gates for quantum computation","volume":"52","author":"Barenco","year":"1995","journal-title":"Phys. Rev. A"},{"key":"ref_15","unstructured":"Nielsen, M., and Chuang, I. (2000). Quantum Computation and Quantum Information, Cambridge University Press."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"875","DOI":"10.1002\/1521-3978(200009)48:9\/11<875::AID-PROP875>3.0.CO;2-V","article-title":"NMR based quantum information processing: Achievements and Prospects","volume":"48","author":"Cory","year":"2000","journal-title":"Fortschr. Phys"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Yan, F., Iliyasu, A., Liu, Z., Abuhasel, K., Jiang, Z., Dong, F., and Hirota, K. (2014, January 16\u201321). Representation of quantum emotion space using Bloch sphere. Hunan, China.","DOI":"10.3390\/e16105290"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3477","DOI":"10.1007\/s11128-013-0612-y","article-title":"Novel image encryption\/decryption based on quantum Fourier transform and double phase encoding","volume":"12","author":"Yang","year":"2013","journal-title":"Quantum Inf. Process"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1802","DOI":"10.1007\/s10773-012-1274-8","article-title":"Quantum image encryption and decryption algorithms based on quantum image geometric transformations","volume":"52","author":"Zhou","year":"2013","journal-title":"Int. J. Theor. Phys"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Venegas-Andraca, S., and Bose, S. (2003, January 21\u201322). Storing, processing and retrieving an image using quantum mechanics. Orlando, FL, USA.","DOI":"10.1117\/12.485960"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s11128-010-0177-y","article-title":"A flexible representation of quantum images for polynomial preparation, image compression, and processing operations","volume":"10","author":"Le","year":"2011","journal-title":"Quantum Inf. Process"},{"key":"ref_22","unstructured":"Latorre, J.I. (2005). Image compression and entanglement. Quantum Phys, arXiv:quant-ph\/0510031."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11128-009-0123-z","article-title":"Processing images in entangled quantum systems","volume":"9","author":"Ball","year":"2010","journal-title":"Quantum Inf. Process"},{"key":"ref_24","unstructured":"Mutze, U. Available online: http:\/\/genie1.ma.utexas.edu\/mp_arc\/c\/08\/08-199.pdf."},{"key":"ref_25","unstructured":"Le, P., Dong, F., and Hirota, K. Flexible Representation of Quantum Images and Its Computational Complexity Analysis. 17\u201319 August 2009."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1007\/978-3-642-11739-8_9","article-title":"A flexible representation and invertible transformations for images on quantum computers","volume":"372","author":"Le","year":"2011","journal-title":"New Adv. Intell. Signal Process"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Sun, B., Le, P., Iliyasu, A., Yan, F., Garcia, J., Dong, F., and Hirota, K. (2011, January 19\u201321). A Multi-Channel Representation for Images on Quantum Computers Using the RGB\u03b1 Color Space. Floriana, Malta.","DOI":"10.1109\/WISP.2011.6051718"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"404","DOI":"10.20965\/jaciii.2013.p0404","article-title":"An RGB multi-channel representation for images on quantum computers","volume":"17","author":"Sun","year":"2013","journal-title":"J. Adv. Comput. Intell. Intell. Inf"},{"key":"ref_29","first-page":"113","article-title":"Fast geometric transformations on quantum images","volume":"40","author":"Le","year":"2010","journal-title":"IAENG Int. J. Appl. Math"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"698","DOI":"10.20965\/jaciii.2011.p0698","article-title":"Efficient colour transformations on quantum image","volume":"15","author":"Le","year":"2011","journal-title":"J. Adv. Comput. Intell. Intell. Inf"},{"key":"ref_31","unstructured":"Sun, B., Iliyasu, A., Yan, F., Garcia, J., Dong, F., Al-Asmari, A., and Hirota, K. (July, January 28). Quantum computation based color information transformation on multi-channel image. Beijing, China."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"140","DOI":"10.20965\/jaciii.2014.p0140","article-title":"Multi-channel information operations on quantum images","volume":"18","author":"Sun","year":"2014","journal-title":"J. Adv. Comput. Intell. Intell. Inf"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.ins.2011.09.028","article-title":"Watermarking and authentication of quantum images based on restricted geometric transformations","volume":"186","author":"Iliyasu","year":"2012","journal-title":"Inf. Sci"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1504\/IJICA.2013.053179","article-title":"A two-tier scheme for greyscale quantum image watermarking and recovery","volume":"5","author":"Iliyasu","year":"2013","journal-title":"Int. J. Innov. Comput. Appl"},{"key":"ref_35","unstructured":"Iliyasu, A., Le, P.F.D., and Hirota, K. (2010, January 27\u201331). Restricted geometric transformations and their applications for quantum image watermarking and authentication. Tokyo, Japan."},{"key":"ref_36","unstructured":"Yan, F., Le, P., Iliyasu, A., Sun, B., Garcia, J., Dong, F., and Hirota, K. (2012, January 10\u201315). Assessing the Similarity of Quantum Images Based on Probability Measurements. Brisbane, Australia."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1504\/IJICA.2013.062955","article-title":"A parallel comparison of multiple pairs of images on quantum computers","volume":"5","author":"Yan","year":"2013","journal-title":"Int. J. Innov. Comput. Appl"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"55","DOI":"10.4236\/jqis.2012.23010","article-title":"Quantum image searching based on probability distributions","volume":"2","author":"Yan","year":"2012","journal-title":"J. Quantum Inf. Sci"},{"key":"ref_39","unstructured":"Iliyasu, A., Le, P., Dong, F., and Hirota, K. (2010, January 25\u201326). A framework for quantum movie representation and production. Tokyo, Japan."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1406","DOI":"10.1016\/j.tcs.2010.11.029","article-title":"Strategies for designing geometric transformations on quantum images","volume":"412","author":"Le","year":"2011","journal-title":"Theor. Comput. Sci"},{"key":"ref_41","unstructured":"Le, P., Iliyasu, A., Dong, F., and Hirota, K. (2010, January 25\u201326). Single qubit color transformations on quantum images. Tokyo, Japan."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"3537","DOI":"10.3390\/e16063537","article-title":"Hybrid quantum-classical protocol for storage and retrieval of discrete-valued information","volume":"16","author":"Iliyasu","year":"2014","journal-title":"Entropy"},{"key":"ref_43","unstructured":"Lomont, C. (2003). Quantum convolution and quantum correlation algorithms are physically impossible. Quantum Phys, arXiv:quant-ph\/0309070."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"020301","DOI":"10.1103\/PhysRevA.82.020301","article-title":"Ancilla-driven universal quantum computation","volume":"82","author":"Anders","year":"2010","journal-title":"Phys. Rev. A"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1103\/PhysRevLett.79.325","article-title":"Quantum mechanics helps in searching for a needle in a haystack","volume":"79","author":"Grover","year":"1997","journal-title":"Phys. Rev. Lett"},{"key":"ref_46","unstructured":"Inoue, M. (2004, January 29). On the Need for Annotation-based Image Retrieval. Sheffield UK."},{"key":"ref_47","first-page":"1","article-title":"Quantum and classical coincidence imaging","volume":"92","author":"Bennink","year":"2004","journal-title":"Phys. Rev. Lett"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Chary, R., Lakshmi, D., and Sunitha, K. (2012, January 21\u201322). Image Searching Based on Image Mean Distance Method. Tamilnadu, India.","DOI":"10.1109\/ICRCC.2012.6450576"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1007\/s11128-012-0423-6","article-title":"A watermark strategy for quantum images based on quantum Fourier transform","volume":"12","author":"Zhang","year":"2013","journal-title":"Quantum Inf. Process"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Yan, F., Iliyasu, A., Venegas-Andraca, S., Dong, F., and Hirota, K. (2014). A duple watermarking strategy for multi-channel quantum images. Quantum Inf. Process, submitted.","DOI":"10.1007\/s11128-014-0912-x"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"2874","DOI":"10.3390\/e15082874","article-title":"Towards realising secure and efficient image and video processing applications on quantum computers","volume":"15","author":"Iliyasu","year":"2013","journal-title":"Entropy"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Yan, F., Iliyasu, A., Venegas-Andraca, S., and Yang, H. (2014). Video encryption and decryption on quantum computers. Int. J. Theor. Phys, submitted.","DOI":"10.1007\/s10773-015-2524-3"},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Jiang, N., and Wang, L. (2014). A novel stratety for quantum image steganography based on Moir\u00e9 Pattern. Int. J. Theor. Phys.","DOI":"10.1007\/s10773-014-2294-3"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.image.2009.11.002","article-title":"Secure reversible visible image watermarking with authentication","volume":"25","author":"Tsai","year":"2010","journal-title":"Signal Process. Image Commun"},{"key":"ref_55","first-page":"11","article-title":"Direct and inverse fuzzy transforms for coding\/decoding color images in YUV space","volume":"3","author":"Loia","year":"2009","journal-title":"J. Uncertain Syst"},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Luthon, F., Beaumesnil, B., and Dubois, N. (2010, January 28\u201330). LUX Color Transform for Mosaic Image Rendering. Cluj-Napoca, Romania.","DOI":"10.1109\/AQTR.2010.5520671"},{"key":"ref_57","first-page":"125","article-title":"Insights into the viability of using available photonic quantum technologies for efficient image and video processing applications","volume":"9","author":"Iliyasu","year":"2013","journal-title":"Int. J. Unconv. Comput"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"3489","DOI":"10.1103\/PhysRevA.52.3489","article-title":"Simple quantum computer","volume":"52","author":"Chuang","year":"1995","journal-title":"Phys. Rev. A"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1103\/RevModPhys.79.135","article-title":"Linear optical quantum computing with photonic qubits","volume":"79","author":"Kok","year":"2007","journal-title":"Rev. Mod. Phys"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1038\/46503","article-title":"Demonstrating the viability of universal quantum computation using teleportation and sigle-qubit operations","volume":"402","author":"Gottesman","year":"1999","journal-title":"Nature"},{"key":"ref_61","unstructured":"Bellini, M. (2011, January 8\u201312). Single-Photon-Level Light Manipulation and Amplification. Toronto, ON, USA."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"1567","DOI":"10.1126\/science.1142892","article-title":"Optical quantum computing","volume":"318","year":"2007","journal-title":"Science"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/10\/5290\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:16:47Z","timestamp":1760217407000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/10\/5290"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10,10]]},"references-count":62,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2014,10]]}},"alternative-id":["e16105290"],"URL":"https:\/\/doi.org\/10.3390\/e16105290","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,10,10]]}}}