Quantum Pattern Search with Closed Match
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Abstract
This paper we proposed a quantum pattern search algorithm based on Grover’s algorithm with closed match. Compared to QuAM proposed by Dan Ventura and QuAM with distributed queries proposed by Ezhov, our algorithm could not only resolve completion problem but also retrieved the full information of the query pattern which only known partial information with non-negligible probability. The algorithm took advantage of the encoding for the pattern set. Moreover we transformed the encoding of each pattern in set to encode all the pattern match cases in order to reduce the cost of encoding. Thus, the nontrivial initial state brought a new method to realize quantum pattern search with a series of proper unitary operations. The simulation result of experiments was also proved that our algorithm was useful and efficient.
Keywords
Quantum pattern search Grover’s algorithm Closed matchNotes
Acknowledgements
This work is supported by the National Natural Science Foundation of China under Grant No. 61065002, the Foundation of Talent of Jinggang of Jiangxi Province under Grant No. 20112BCB23014, Project of International Cooperation and Exchanges of Jiangxi Province under Grant No. 20112BDH80007, Project of International Cooperation and Exchanges of Nanchang City, the item of science and technology awarded by Education Bureau of Jiangxi Province under Grant No. GJJ12433.
References
- 1.Deutsch, D., Jozsa, R.: Rapid solution of problems by quantum computation. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 439(1907), 553–558 (1992) MathSciNetADSCrossRefMATHGoogle Scholar
- 2.Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 124–134. IEEE, New York (1994). CrossRefGoogle Scholar
- 3.Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 212–219. ACM, New York (1996) CrossRefGoogle Scholar
- 4.Boyer, M., Brassard, G., Høyer, P., et al.: Tight bounds on quantum searching (1996). arXiv:quant-ph/9605034
- 5.Ventura, D.: Artificial associative memory using quantum processes. In: Proceedings of the International Conference on Computational Intelligence and Neuroscience, vol. 2, pp. 218–221 (1998) Google Scholar
- 6.Ventura, D., Martinez, T.: Quantum associative memory. Inf. Sci. 124(1), 273–296 (2000) MathSciNetCrossRefGoogle Scholar
- 7.Ventura, D., Martinez, T.: Initializing the amplitude distribution of a quantum state. Found. Phys. Lett. 12(6), 547–559 (1999) MathSciNetCrossRefGoogle Scholar
- 8.Ventura, D., Martinez, T.: A quantum associative memory based on Grover’s algorithm. In: Artificial Neural Nets and Genetic Algorithms, pp. 22–27. Springer, Vienna (1999) CrossRefGoogle Scholar
- 9.Ezhov, A.A., Nifanova, A.V., Ventura, D.: Quantum associative memory with distributed queries. Inf. Sci. 128(3), 271–293 (2000) MathSciNetCrossRefMATHGoogle Scholar
- 10.Mateus, P., Omar, Y.: Quantum pattern matching (2005). arXiv:quant-ph/0508237
- 11.Angelakis, D.G.: A quantum algorithm for closest pattern matching. Quantum Inf. Process. 199, 180 (2006) Google Scholar
- 12.Zhou, R., Ding, Q.: Quantum pattern recognition with probability of 100 %. Int. J. Theor. Phys. 47(5), 1278–1285 (2008) MathSciNetCrossRefMATHGoogle Scholar
- 13.Rigui, Z., Nan, J., Qiulin, D.: Model and training of QNN with weight. Neural Process. Lett. 24(3), 261–269 (2006) CrossRefGoogle Scholar
- 14.Zhou, R., Ding, Q.: Quantum MP neural network. Int. J. Theor. Phys. 46(12), 3209–3215 (2007) MathSciNetCrossRefMATHGoogle Scholar
- 15.Zhou, R.: Quantum competitive neural network. Int. J. Theor. Phys. 49(1), 110–119 (2010) CrossRefMATHGoogle Scholar
- 16.Zhou, R., Wang, H., Wu, Q., et al.: Quantum associative neural network with nonlinear search algorithm. Int. J. Theor. Phys. 51(3), 705–723 (2012) CrossRefMATHGoogle Scholar
- 17.Njafa, J.P.T., Engo, S.G.N., Woafo, P.: Quantum associative memory with improved distributed queries. Int. J. Theor. Phys. 1–15 (2012) Google Scholar