Abstract
The operations of data set, such as intersection, union and complement, are the fundamental calculation in mathematics. It’s very significant that designing fast algorithm for set operation. In this paper, the quantum algorithm for calculating intersection set \({\text{C}=\text{A}\cap \text{B}}\) is presented. Its runtime is \({O\left( {\sqrt{\left| A \right|\times \left| B \right|\times \left|C \right|}}\right)}\) for case \({\left| C \right|\neq \phi}\) and \({O\left( {\sqrt{\left| A \right|\times \left| B \right|}}\right)}\) for case \({\left| C \right|=\phi}\) (i.e. C is empty set), while classical computation needs O (|A| × |B|) steps of computation in general, where |.| denotes the size of set. The presented algorithm is the combination of Grover’s algorithm, classical memory and classical iterative computation, and the combination method decrease the complexity of designing quantum algorithm. The method can be used to design other set operations as well.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Tang S.-F.: Computer Organization and Architecture, 2nd edn. Higher Education Press, Beijing (2000)
Shor, P.W.: Algorithms for quantum computation discretelog and factoring. In: Proceedings of the 35th Annual Symposium on the Foundations of Computer Science, Los Alamitos, pp. 20–24 (1994)
Vandersypen L.M.K., Steffen M., Breytal G., Yannonil C.S., Sherwood M.H., Chuang I.L.: Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonace, information and computation: classical and quantum aspects. Nature 414, 883–887 (2001)
Lu C.-Y., Browne D.E., Yang T., Pan J.-W.: Demonstration of a compiled version of shor’s quantum factoring algorithm using photonic qubits. Phys. Rev. Lett. 99, 250504 (2007)
Pang, C.-Y., Ding, C.-B., Hu, B.-Q.: Quantum pattern recongnition of classical signal (2007). arXiv: quant-ph/0707.0936
Pang, C.Y.: Loading N-dimensional vector into quantum registers from classical memory with O (logN) Steps (2006). arXiv:quant-ph/0612061
Latorre, J.I.: Imange compression and entanglement (2005). arXiv:quant-ph/0510031
Pang, C.-Y.: Quantum image compression, Postdoctoral report, Key Laboratory of Quantum Information, Uni. of Science and Technology of China (CAS) Hefei, China (2006)
Pang C.-Y., Zhou Z.-W., Guo G.-C.: A hybrid quantum encoding algorithm of vector quantization for image compression. Chin. Phys. 15, 3039–3043 (2006)
Pang C.-Y., Zhou Z.-W., Chen P.-X., Guo G.-C.: Design of quantum vq iteration and quantum vq encoding algorithm taking sqrt(n) steps for data compression. Chin. phys. 15, 618–623 (2006)
Pang, C.-Y., Hu, B.-Q.: Quantum discrete fourier tranform with classical output for signal processing (2007). arXiv:quant-ph/0706.2451
Pang, C.-Y., Zhou, Z.-W., Guo, G.-C.: Quantum discrete cosine transform for image compression (2006). arxiv:quant-ph/0601043
Nielsen M.A., Chuang I.L.: Quantum Computationand and Quantum Information, 1st edn. Cambridge University Press, Cambridge (2000)
Giovannetti, V., Lloyd, S., Maccone, L.: Quantum random access memory (2007). arXiv:quant-ph/0708.1879
Grover, L.K.: Afast quantum mechanical algorithm for database search. In: Proceedings of the Twenty- Eighth Annual ACM Symposium on the Theory of Computing, Philadelphia, Pennsylvania, pp. 212–219 (1996)
Boyer M., Brassard G., Hoyer P., Tap A.: Tight bounds on quantum searching. Fortsch. Phys. 46, 493–506 (1998)
Durr, C., Hoyer, P.: A quantum algorithm for finding the minimun (1996). arXiv:quant-ph/9607014
Long G.L.: Grover algorithm with zero theoretical failure rate. Phys. Rev. A 64, 022307 (2001)
Biham E., Biham O., Biron D., Grassl M., Lidar D.A.: Grover’s quantum search algorithm for an arbitary initial amplitude distribution. Phys. Rev. A 60, 2742–2745 (1999)
Biham E., Biham O., Biron D., Grassl M., Lidar D.A., Shapira D.: Analysis of generalized Grover quantum search algorithm using recursion equations. Phys. Rev. A 63, 012310 (2000)
Parka S., Baeb J., Kwon Y.: Wavelet quantum search algorithm with partial information. J. Chaos Solitons Fractals 32(4), 1371–1374 (2007)
Tulsi A.: Faster quantum-walk algorithm for the two-dimensional spatial search. J. Phys. Rev. A 78(1), 7–13 (2008)
korepin V. E.: Quantum search algorithms. Int. J. Mod. Phys. B 23(31), 5727–5758 (2009)
Ambainis A.: Quantum search with variable times. J. Theory Comput. Syst. 47(3), 786–807 (2010)
Zhou R., Ding Q.: Quantum pattern recognition with probability of 100%. Int. J. Theor. Phys. 47(5), 1278–1285 (2008)
Rigui Z., Jiang N., Ding Q.: Model and training of QNN with weight. Neural Process. Lett. 24(3), 261–269 (2006)
Zhou R., Ding Q.: Quantum M-P neural network. Int. J. Theor. Phys. 46(12), 3209–3215 (2007)
Zhou R.: Quantum competitive neural network. Int. J. Theor. Phys. 49(1), 110–119 (2010)
Younes, A.: Fixed phase quantum search algorithm. J. Quant-ph/0704.1585, 1–8
Li P.C., Li S.Y.: Two improvements in Grover’s algorithm. Chin. J. Electron. 17(1), 100–104 (2008)
Li P.C., Li S.Y.: A Grover quantum searching algorithm based on the weighted targets. J. Syst. Eng. Electron. 19(2), 363–369 (2008)
Rungta P.: The quadratic speedup in Grover’s search algorithm from the entanglement perspective. Phys. Lett. A 373(31), 2652–2659 (2009)
Liang H., Dan L., GuiLu L.: An N/4 fixed-point duality quantum search algorithm. Sci. China Phys. Mech. Astron. 53(9), 1765–1768 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pang, CY., Zhou, RG., Ding, CB. et al. Quantum search algorithm for set operation. Quantum Inf Process 12, 481–492 (2013). https://doi.org/10.1007/s11128-012-0385-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11128-012-0385-8