{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,29]],"date-time":"2025-11-29T16:21:27Z","timestamp":1764433287106},"reference-count":64,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2019,10,26]],"date-time":"2019-10-26T00:00:00Z","timestamp":1572048000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,10,26]],"date-time":"2019-10-26T00:00:00Z","timestamp":1572048000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Youth Science Foundation of Northeast Petroleum University","award":["2018QNL-08"],"award-info":[{"award-number":["2018QNL-08"]}]},{"name":"Guiding Innovation Fund of Northeast Petroleum University","award":["2018YDL-20"],"award-info":[{"award-number":["2018YDL-20"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2019,12]]},"DOI":"10.1007\/s11128-019-2479-z","type":"journal-article","created":{"date-parts":[[2019,10,26]],"date-time":"2019-10-26T14:04:32Z","timestamp":1572098672000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Quantum circuit design for several morphological image processing methods"],"prefix":"10.1007","volume":"18","author":[{"given":"Panchi","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tong","family":"Shi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aiping","family":"Lu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bing","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,10,26]]},"reference":[{"key":"2479_CR1","unstructured":"Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceeding of 35th Annual Symposium Foundations of Computer Science, pp. 124\u2013134. IEEE Computer Society Press, Los Almitos(1994)"},{"key":"2479_CR2","doi-asserted-by":"crossref","unstructured":"Grover, L.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, pp. 212\u2013219 (1996)","DOI":"10.1145\/237814.237866"},{"key":"2479_CR3","unstructured":"Beach, G., Lomont, C., Cohen, C.: Quantum image processing (QuIP). In: Proceedings of the 32nd IEEE Conference on Applied Imagery and Pattern Recognition, pp. 39\u201344. Bellingham, WA, USA (2003)"},{"issue":"3","key":"2479_CR4","first-page":"1730001-(1-18)","volume":"15","author":"F Yan","year":"2017","unstructured":"Yan, F., Iliyasu, A.M., Le, P.Q.: Quantum image processing: a review of advances in its security technologies. Int. J. Quantum Inf. 15(3), 1730001-(1-18) (2017)","journal-title":"Int. J. Quantum Inf."},{"key":"2479_CR5","doi-asserted-by":"crossref","unstructured":"Venegas-Andraca, S., Bose, S.: Storing, processing, and retrieving an image using quantum mechanics. In: Proceedings of SPIE Conference of Quantum Information and Computation, vol. 5105, pp. 134\u2013147 (2003)","DOI":"10.1117\/12.485960"},{"key":"2479_CR6","unstructured":"Latorre, J.: Image Compression and Entanglement (2005). \narXiv:quant-ph\/0510031"},{"issue":"1","key":"2479_CR7","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s11128-010-0177-y","volume":"10","author":"PQ Le","year":"2011","unstructured":"Le, P.Q., Dong, F., Hirota, K.: A flexible representation of quantum images for polynomial preparation, image compression, and processing operations. Quantum Inf. Process. 10(1), 63\u201384 (2011)","journal-title":"Quantum Inf. Process."},{"issue":"6","key":"2479_CR8","doi-asserted-by":"crossref","first-page":"1353","DOI":"10.1007\/s11128-014-0733-y","volume":"13","author":"S Yuan","year":"2014","unstructured":"Yuan, S., Mao, X., Xue, Y., Chen, L., Xiong, Q., Compare, A.: SQR: a simple quantum representation of infrared images. Quantum Inf. Process. 13(6), 1353\u20131379 (2014)","journal-title":"Quantum Inf. Process."},{"issue":"3","key":"2479_CR9","doi-asserted-by":"crossref","first-page":"404","DOI":"10.20965\/jaciii.2013.p0404","volume":"17","author":"B Sun","year":"2013","unstructured":"Sun, B., Iliyasu, A., Yan, F., Dong, F., Hirota, K.: An RGB multi-channel representation for images on quantum computers. J. Adv. Comput. Intell. Intell. Info. 17(3), 404\u2013417 (2013)","journal-title":"J. Adv. Comput. Intell. Intell. Info."},{"key":"2479_CR10","doi-asserted-by":"crossref","unstructured":"Sun, B., Le, P., Iliyasu, A., Yan, F., Garcia, J., Dong, F., Hirota, K.: Amulti-channel representation for images on quantum computers using the RGB color space. In: IEEE 7th International Symposium on Intelligent Signal Processing (WISP), pp. 1\u20136 (2011)","DOI":"10.1109\/WISP.2011.6051718"},{"issue":"8","key":"2479_CR11","doi-asserted-by":"crossref","first-page":"2833","DOI":"10.1007\/s11128-013-0567-z","volume":"12","author":"Y Zhang","year":"2013","unstructured":"Zhang, Y., Lu, K., Gao, Y., et al.: NEQR: a novel enhanced quantum representation of digital images. Quantum Inf. Process. 12(8), 2833\u20132860 (2013)","journal-title":"Quantum Inf. Process."},{"issue":"4","key":"2479_CR12","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1007\/s11128-012-0423-6","volume":"12","author":"WW Zhang","year":"2013","unstructured":"Zhang, W.W., Gao, F., Liu, B., et al.: A watermark strategy for quantum images based on quantum Fourier transformation. Quantum Inf. Process. 12(4), 793\u2013803 (2013)","journal-title":"Quantum Inf. Process."},{"issue":"2","key":"2479_CR13","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1007\/s10773-012-1354-9","volume":"52","author":"WW Zhang","year":"2013","unstructured":"Zhang, W.W., Gao, F., Liu, B., et al.: A quantum watermark protocol. Int. J. Theor. Phys. 52(2), 504\u2013513 (2013)","journal-title":"Int. J. Theor. Phys."},{"issue":"5","key":"2479_CR14","doi-asserted-by":"crossref","first-page":"1223","DOI":"10.1007\/s11128-013-0721-7","volume":"13","author":"N Jiang","year":"2014","unstructured":"Jiang, N., Wu, W.Y., Wang, L.: The quantum realization of Arnold and Fibonacci image scrambling. Quantum Inf. Process. 13(5), 1223\u20131236 (2014)","journal-title":"Quantum Inf. Process."},{"issue":"7","key":"2479_CR15","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1007\/s11128-014-0749-3","volume":"13","author":"N Jiang","year":"2014","unstructured":"Jiang, N., Wang, L.: Analysis and improvement of the quantum Arnold image scrambling. Quantum Inf. Process. 13(7), 1545\u20131551 (2014)","journal-title":"Quantum Inf. Process."},{"issue":"7","key":"2479_CR16","doi-asserted-by":"crossref","first-page":"2463","DOI":"10.1007\/s10773-014-2046-4","volume":"53","author":"N Jiang","year":"2014","unstructured":"Jiang, N., Wang, L., Wu, W.Y.: Quantum Hilbert image scrambling. Int. J. Theor. Phys. 53(7), 2463\u20132484 (2014)","journal-title":"Int. J. Theor. Phys."},{"issue":"5","key":"2479_CR17","doi-asserted-by":"crossref","first-page":"1717","DOI":"10.1007\/s11128-015-0964-6","volume":"14","author":"RG Zhou","year":"2015","unstructured":"Zhou, R.G., Sun, Y.J., Fan, P.: Quantum image Gray-code and bit-plane scrambling. Quantum Inf. Process. 14(5), 1717\u20131734 (2015)","journal-title":"Quantum Inf. Process."},{"issue":"4","key":"2479_CR18","doi-asserted-by":"crossref","first-page":"1193","DOI":"10.1007\/s11128-015-0926-z","volume":"14","author":"NR Zhou","year":"2015","unstructured":"Zhou, N.R., Hua, T.X., Gong, L.H., et al.: Quantum image encryption based on generalized Arnold transform and double random-phase encoding. Quantum Inf. Process. 14(4), 1193\u20131213 (2015)","journal-title":"Quantum Inf. Process."},{"issue":"6","key":"2479_CR19","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/s11128-018-1902-1","volume":"17","author":"NR Zhou","year":"2018","unstructured":"Zhou, N.R., Chen, W.W., Yan, X.Y., et al.: Bit-level quantum color image encryption scheme with quantum cross-exchange operation and hyper-chaotic system. Quantum Inf. Process. 17(6), 137 (2018)","journal-title":"Quantum Inf. Process."},{"issue":"7","key":"2479_CR20","doi-asserted-by":"crossref","first-page":"3234","DOI":"10.1007\/s10773-016-2954-6","volume":"55","author":"LH Gong","year":"2016","unstructured":"Gong, L.H., He, X.T., Cheng, S., et al.: Quantum image encryption algorithm based on quantum image XOR operations. Int. J. Theor. Phys. 55(7), 3234\u20133250 (2016)","journal-title":"Int. J. Theor. Phys."},{"key":"2479_CR21","first-page":"243","volume":"2","author":"S Wang","year":"2014","unstructured":"Wang, S., Song, X.H., Niu, X.M.: A novel encryption algorithm for quantum images based on quantum wavelet transform and diffusion. Intell. Data Anal. Appl. 2, 243\u2013250 (2014)","journal-title":"Intell. Data Anal. Appl."},{"issue":"8","key":"2479_CR22","doi-asserted-by":"crossref","first-page":"1765","DOI":"10.1007\/s11128-014-0768-0","volume":"13","author":"XH Song","year":"2014","unstructured":"Song, X.H., Wang, S., Ahmed, A., et al.: Quantum image encryption based on restricted geometric and color transformations. Quantum Inf. Process. 13(8), 1765\u20131787 (2014)","journal-title":"Quantum Inf. Process."},{"issue":"6","key":"2479_CR23","doi-asserted-by":"crossref","first-page":"1802","DOI":"10.1007\/s10773-012-1274-8","volume":"52","author":"RG Zhou","year":"2013","unstructured":"Zhou, R.G., Wu, Q., Zhang, M.Q., et al.: Quantum image encryption and decryption algorithms based on quantum image geometric transformations. Int. J. Theor. Phys. 52(6), 1802\u20131817 (2013)","journal-title":"Int. J. Theor. Phys."},{"issue":"12","key":"2479_CR24","doi-asserted-by":"crossref","first-page":"4653","DOI":"10.1016\/j.cnsns.2012.05.033","volume":"17","author":"A Akhshani","year":"2012","unstructured":"Akhshani, A., Akhavan, A., Lim, S.C., et al.: An image encryption scheme based on quantum logistic map. Commun. Nonlinear Sci. Numer. Simul. 17(12), 4653\u20134661 (2012)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"issue":"11","key":"2479_CR25","doi-asserted-by":"crossref","first-page":"3477","DOI":"10.1007\/s11128-013-0612-y","volume":"12","author":"YG Yang","year":"2013","unstructured":"Yang, Y.G., Xia, J., Jia, X., et al.: Novel image encryption\/decryption based on quantum Fourier transform and double phase encoding. Quantum Inf. Process. 12(11), 3477\u20133493 (2013)","journal-title":"Quantum Inf. Process."},{"issue":"6","key":"2479_CR26","doi-asserted-by":"crossref","first-page":"1961","DOI":"10.1007\/s10773-017-3341-7","volume":"56","author":"PC Li","year":"2017","unstructured":"Li, P.C., Zhao, Y.: A simple encryption algorithm for quantum color image. Int. J. Theor. Phys. 56(6), 1961\u20131982 (2017)","journal-title":"Int. J. Theor. Phys."},{"issue":"8","key":"2479_CR27","doi-asserted-by":"crossref","first-page":"2893","DOI":"10.1007\/s10773-015-2524-3","volume":"54","author":"F Yan","year":"2015","unstructured":"Yan, F., Iliyasu, A., Salvador, E., et al.: Video encryption and decryption on quantum computers. Int. J. Theor. Phys. 54(8), 2893\u20132904 (2015)","journal-title":"Int. J. Theor. Phys."},{"issue":"1","key":"2479_CR28","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.ins.2011.09.028","volume":"186","author":"A Iliyasu","year":"2012","unstructured":"Iliyasu, A., Le, P.Q., Dong, F.Y., et al.: Watermarking and authentication of quantum image based on restricted geometric transformations. Inf. Sci. 186(1), 126\u2013149 (2012)","journal-title":"Inf. Sci."},{"issue":"5","key":"2479_CR29","doi-asserted-by":"crossref","first-page":"1675","DOI":"10.1007\/s11128-014-0912-x","volume":"14","author":"F Yan","year":"2015","unstructured":"Yan, F., Iliyasu, A., Sun, B., et al.: A duple watermarking strategy for multi-channel quantum images. Quantum Inf. Process. 14(5), 1675\u20131692 (2015)","journal-title":"Quantum Inf. Process."},{"issue":"8","key":"2479_CR30","doi-asserted-by":"crossref","first-page":"2765","DOI":"10.1007\/s11128-013-0561-5","volume":"12","author":"YG Yang","year":"2013","unstructured":"Yang, Y.G., Jia, X., Xu, P., et al.: Analysis and improvement of the watermark strategy for quantum image based on quantum Fourier transform. Quantum Inf. Process. 12(8), 2765\u20132769 (2013)","journal-title":"Quantum Inf. Process."},{"issue":"12","key":"2479_CR31","doi-asserted-by":"crossref","first-page":"3689","DOI":"10.1007\/s11128-013-0629-2","volume":"12","author":"XH Song","year":"2013","unstructured":"Song, X.H., Wang, S., Liu, S., et al.: A dynamic watermarking scheme for quantum images using quantum wavelet transform. Quantum Inf. Process. 12(12), 3689\u20133706 (2013)","journal-title":"Quantum Inf. Process."},{"issue":"4","key":"2479_CR32","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/s00530-014-0355-3","volume":"20","author":"XH Song","year":"2014","unstructured":"Song, X.H., Wang, S., Niu, X.M., et al.: Dynamic watermarking scheme for quantum images based on Hadamard transform. Multimedia Syst. 20(4), 379\u2013388 (2014)","journal-title":"Multimedia Syst."},{"issue":"11","key":"2479_CR33","doi-asserted-by":"crossref","first-page":"4415","DOI":"10.1007\/s11128-016-1413-x","volume":"15","author":"PC Li","year":"2016","unstructured":"Li, P.C., Xiao, H., Li, B.X.: Quantum representation and watermark strategy for color images based on the controlled rotation of qubits. Quantum Inf. Process. 15(11), 4415\u20134440 (2016)","journal-title":"Quantum Inf. Process."},{"issue":"10","key":"2479_CR34","doi-asserted-by":"crossref","first-page":"4205","DOI":"10.1007\/s10773-016-3046-3","volume":"55","author":"H Shahrokh","year":"2016","unstructured":"Shahrokh, H., Mosayeb, N.: A novel LSB based quantum watermarking. Int. J. Theor. Phys. 55(10), 4205\u20134218 (2016)","journal-title":"Int. J. Theor. Phys."},{"issue":"5","key":"2479_CR35","doi-asserted-by":"crossref","first-page":"1849","DOI":"10.1007\/s11128-016-1260-9","volume":"15","author":"S Miyake","year":"2016","unstructured":"Miyake, S., Nakamae, K.: A quantum watermarking scheme using simple and small-scale quantum circuits. Quantum Inf. Process. 15(5), 1849\u20131864 (2016)","journal-title":"Quantum Inf. Process."},{"issue":"5","key":"2479_CR36","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s11128-017-1577-z","volume":"16","author":"PC Li","year":"2017","unstructured":"Li, P.C., Zhao, Y., Xiao, H., et al.: An improved quantum watermarking scheme using small-scale quantum circuits and color scrambling. Quantum Inf. Process. 16(5), 127 (2017)","journal-title":"Quantum Inf. Process."},{"issue":"9","key":"2479_CR37","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1007\/s11128-017-1640-9","volume":"16","author":"RG Zhou","year":"2017","unstructured":"Zhou, R.G., Hu, W.W., Fan, P.: Quantum watermarking scheme through Arnold scrambling and LSB steganography. Quantum Inf. Process. 16(9), 212 (2017)","journal-title":"Quantum Inf. Process."},{"issue":"6","key":"2479_CR38","first-page":"77","volume":"139","author":"N Mosayeb","year":"2017","unstructured":"Mosayeb, N., Shahrokh, H., Masoud, B., et al.: A new secure quantum watermarking scheme. Optik 139(6), 77\u201386 (2017)","journal-title":"Optik"},{"issue":"11","key":"2479_CR39","doi-asserted-by":"crossref","first-page":"3460","DOI":"10.1007\/s10773-017-3512-6","volume":"56","author":"ZG Qu","year":"2017","unstructured":"Qu, Z.G., Cheng, Z.W., Luo, M.X., et al.: A robust quantum watermark algorithm based on quantum log-polar images. Int. J. Theor. Phys. 56(11), 3460\u20133476 (2017)","journal-title":"Int. J. Theor. Phys."},{"issue":"3","key":"2479_CR40","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1007\/s10773-014-2294-3","volume":"54","author":"N Jiang","year":"2015","unstructured":"Jiang, N., Wang, L.: A novel strategy for quantum image steganography based on Moire pattern. Int. J. Theor. Phys. 54(3), 1021\u20131032 (2015)","journal-title":"Int. J. Theor. Phys."},{"issue":"1","key":"2479_CR41","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/s10773-015-2640-0","volume":"55","author":"N Jiang","year":"2016","unstructured":"Jiang, N., Zhao, N., Wang, L.: LSB based quantum image steganography algorithm. Int. J. Theor. Phys. 55(1), 107\u2013123 (2016)","journal-title":"Int. J. Theor. Phys."},{"issue":"11","key":"2479_CR42","doi-asserted-by":"crossref","first-page":"4441","DOI":"10.1007\/s11128-016-1411-z","volume":"15","author":"JZ Sang","year":"2016","unstructured":"Sang, J.Z., Wang, S., Li, Q.: Least significant qubit algorithm for quantum images. Quantum Inf. Process. 15(11), 4441\u20134460 (2016)","journal-title":"Quantum Inf. Process."},{"key":"2479_CR43","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1016\/j.measurement.2015.05.038","volume":"73","author":"S Wang","year":"2015","unstructured":"Wang, S., Sang, J.Z., Song, X.H., et al.: Least significant qubit (LSQb) information hiding algorithm for quantum image. Measurement 73, 352\u2013359 (2015)","journal-title":"Measurement"},{"issue":"5","key":"2479_CR44","doi-asserted-by":"crossref","first-page":"1750039","DOI":"10.1142\/S0219749917500393","volume":"15","author":"N Mosayeb","year":"2017","unstructured":"Mosayeb, N., Monireh, H.: Quantum red\u2013green\u2013blue image steganography. Int. J. Quantum Inf. 15(5), 1750039 (2017)","journal-title":"Int. J. Quantum Inf."},{"issue":"10","key":"2479_CR45","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1007\/s11128-017-1694-8","volume":"16","author":"H Shahrokh","year":"2017","unstructured":"Shahrokh, H., Ehsan, F.: A novel quantum LSB-based steganography method using the Gray code for colored quantum images. Quantum Inf. Process. 16(10), 242 (2017)","journal-title":"Quantum Inf. Process."},{"issue":"2","key":"2479_CR46","doi-asserted-by":"crossref","first-page":"1850020","DOI":"10.1142\/S021974991850020X","volume":"16","author":"PC Li","year":"2018","unstructured":"Li, P.C., Liu, X.D.: A novel quantum steganography scheme for color images. Int. J. Quantum Inf. 16(2), 1850020 (2018)","journal-title":"Int. J. Quantum Inf."},{"issue":"5","key":"2479_CR47","doi-asserted-by":"crossref","first-page":"1516","DOI":"10.1007\/s10773-018-3678-6","volume":"57","author":"PC Li","year":"2018","unstructured":"Li, P.C., Lu, A.P.: LSB-based steganography using reflected Gray code for color quantum images. Int. J. Theor. Phys. 57(5), 1516\u20131548 (2018)","journal-title":"Int. J. Theor. Phys."},{"issue":"2","key":"2479_CR48","first-page":"3543","volume":"56","author":"ZG Qu","year":"2017","unstructured":"Qu, Z.G., Chen, S.Y., Ji, S.: A novel quantum video steganography protocol with large payload based on MCQI quantum video. Int. J. Theor. Phys. 56(2), 3543\u20133561 (2017)","journal-title":"Int. J. Theor. Phys."},{"issue":"6","key":"2479_CR49","doi-asserted-by":"crossref","first-page":"1459","DOI":"10.1142\/S0219749911008015","volume":"9","author":"AM Iliyasu","year":"2011","unstructured":"Iliyasu, A.M., Le, P.Q., Dong, F.Y., et al.: A framework for representing and producing movies on quantum computers. Int. J. Quantum Inf. 9(6), 1459\u20131497 (2011)","journal-title":"Int. J. Quantum Inf."},{"key":"2479_CR50","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.tcs.2017.12.025","volume":"752","author":"F Yan","year":"2018","unstructured":"Yan, F., Iliyasu, A.M., Guo, Y.M., Yang, H.M.: Flexible representation and manipulation of audio signals on quantum computers. Theor. Comput. Sci. 752, 71\u201385 (2018)","journal-title":"Theor. Comput. Sci."},{"issue":"9","key":"2479_CR51","doi-asserted-by":"crossref","first-page":"3543","DOI":"10.1007\/s11128-016-1364-2","volume":"15","author":"N Jiang","year":"2016","unstructured":"Jiang, N., Dang, Y., Wang, J.: Quantum image matching. Quantum Inf. Process. 15(9), 3543\u20133572 (2016)","journal-title":"Quantum Inf. Process."},{"issue":"10","key":"2479_CR52","doi-asserted-by":"crossref","first-page":"4501","DOI":"10.1007\/s10773-016-3073-0","volume":"55","author":"N Jiang","year":"2016","unstructured":"Jiang, N., Dang, Y., Zhao, N.: Quantum image location. Int. J. Theor. Phys. 55(10), 4501\u20134512 (2016)","journal-title":"Int. J. Theor. Phys."},{"issue":"3","key":"2479_CR53","first-page":"113","volume":"40","author":"PQ Le","year":"2010","unstructured":"Le, P.Q., Iliyasuy, A.M., Dong, F., et al.: Fast geometric transformations on quantum images. IAENG Int. J. Appl. Math. 40(3), 113\u2013123 (2010)","journal-title":"IAENG Int. J. Appl. Math."},{"issue":"5","key":"2479_CR54","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1007\/s11128-015-0986-0","volume":"14","author":"N Jiang","year":"2015","unstructured":"Jiang, N., Wu, W.Y., Wang, L., et al.: Quantum image pseudo color coding based on the density-stratified method. Quantum Inf. Process. 14(5), 1735\u20131755 (2015)","journal-title":"Quantum Inf. Process."},{"issue":"5","key":"2479_CR55","doi-asserted-by":"crossref","first-page":"1573","DOI":"10.1007\/s11128-014-0842-7","volume":"14","author":"Y Zhang","year":"2015","unstructured":"Zhang, Y., Lu, K., Xu, K., et al.: Local feature point extraction for quantum images. Quantum Inf. Process. 14(5), 1573\u20131588 (2015)","journal-title":"Quantum Inf. Process."},{"issue":"5","key":"2479_CR56","doi-asserted-by":"crossref","first-page":"1693","DOI":"10.1007\/s11128-015-0932-1","volume":"14","author":"C Simona","year":"2015","unstructured":"Simona, C., Vasile, I.M.: Image segmentation on a quantum computer. Quantum Inf. Process. 14(5), 1693\u20131715 (2015)","journal-title":"Quantum Inf. Process."},{"issue":"5","key":"2479_CR57","doi-asserted-by":"crossref","first-page":"1625","DOI":"10.1007\/s11128-014-0862-3","volume":"14","author":"SZ Yuan","year":"2015","unstructured":"Yuan, S.Z., Mao, X., Li, T., et al.: Quantum morphology operations based on quantum representation model. Quantum Inf. Process. 14(5), 1625\u20131645 (2015)","journal-title":"Quantum Inf. Process."},{"issue":"6","key":"2479_CR58","doi-asserted-by":"crossref","first-page":"1974","DOI":"10.1007\/s10773-014-2402-4","volume":"54","author":"RG Zhou","year":"2015","unstructured":"Zhou, R.G., Chang, Z.B., Fan, P., et al.: Quantum image morphology processing based on quantum set operation. Int. J. Theor. Phys. 54(6), 1974\u20131985 (2015)","journal-title":"Int. J. Theor. Phys."},{"issue":"2","key":"2479_CR59","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/s10773-018-3943-8","volume":"58","author":"P Fan","year":"2019","unstructured":"Fan, P., Zhou, R.G., Hu, W.W., et al.: Quantum circuit realization of morphological gradient for quantum grayscale image. Int. J. Theor. Phys. 58(2), 415\u2013435 (2019)","journal-title":"Int. J. Theor. Phys."},{"issue":"9","key":"2479_CR60","first-page":"302","volume":"39","author":"D Wang","year":"2012","unstructured":"Wang, D., Liu, Z., Zhu, W., et al.: Design of quantum comparator based on extended general Toffoli gates with multiple targets. Comput. Sci. 39(9), 302\u2013306 (2012)","journal-title":"Comput. Sci."},{"issue":"1","key":"2479_CR61","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1103\/PhysRevA.54.147","volume":"54","author":"V Vefral","year":"1996","unstructured":"Vefral, V., Barenco, A., Ekert, A.: Quantum networks for elementary arithmetic operations. Phys. Rev. A 54(1), 147\u2013153 (1996)","journal-title":"Phys. Rev. A"},{"issue":"5","key":"2479_CR62","doi-asserted-by":"crossref","first-page":"3457","DOI":"10.1103\/PhysRevA.52.3457","volume":"52","author":"B Adriano","year":"1995","unstructured":"Adriano, B., Charles, H.B., Richard, C., et al.: Elementary gates for quantum computation. Phys. Rev. A 52(5), 3457\u20133467 (1995)","journal-title":"Phys. Rev. A"},{"issue":"9","key":"2479_CR63","doi-asserted-by":"crossref","first-page":"1652","DOI":"10.1109\/TCAD.2005.858352","volume":"25","author":"NN William","year":"2006","unstructured":"William, N.N., Song, X.Y., Yang, G.W., et al.: Optimal synthesis of multiple output boolean functions using a set of quantum gates by symbolic reachability analysis. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 25(9), 1652\u20131663 (2006)","journal-title":"IEEE Trans. Comput. Aided Des. Integr. Circuits Syst."},{"key":"2479_CR64","unstructured":"Himanshu, T., Nagarajan R.: Design of efficient reversible binary subtractors based on a new reversible gate. In: 2009 IEEE Computer Society Annual Symposium on VLSI, pp. 229\u2013234. IEEE Computer Society Press, Tampa, Florida, USA (2009)"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-019-2479-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11128-019-2479-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-019-2479-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,24]],"date-time":"2020-10-24T23:33:47Z","timestamp":1603582427000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11128-019-2479-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,26]]},"references-count":64,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["2479"],"URL":"https:\/\/doi.org\/10.1007\/s11128-019-2479-z","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,26]]},"assertion":[{"value":"30 March 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 October 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 October 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"364"}}