Abstract
Every Boolean function can be presented as a logical formula in conjunctive normal form. Fast algorithm for conjunction plays significant role in overall algorithm for computing arbitrary Boolean function. First, we present a quantum query algorithm for conjunction of two bits. Our algorithm uses one quantum query and correct result is obtained with a probability p = 4/5, that improves the previous result. Then, we present the main result - generalization of our approach to design efficient quantum algorithms for computing conjunction of two Boolean functions. Finally, we demonstrate another kind of an algorithm for conjunction of two bits, that has a correct answer probability p = 9/10. This algorithm improves success probability by 10%, but stands aside and cannot be extended to compute conjunction of Boolean functions.
This research was supported by Grant No. 09.1570 from the Latvian Council of Science and by Project Nr. 2009/0138/1DP/1.1.2.1.2/09/IPIA/VIAA/004 from the European Social Fund.
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
Shor, P.W.: Polynomial time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing 26(5), 1484–1509 (1997)
Grover, L.: A fast quantum mechanical algorithm for database search. In: Proceedings of 28th STOC 1996, pp. 212–219 (1996)
Calude, C.S.: Information and Randomness: an Algorithmic Perspective, 2nd edn. Springer, Heidelberg (2002)
Calude, C.S., Pavlov, B.: Coins, quantum measurements and Turing’s barrier. Quantum Information Processing 1(1-2), 107–127 (2002)
Calude, C.S., Stay, M.A.: Natural halting probabilities, partial randomness and zeta functions. Information and Computation 204(11), 1718–1739 (2006)
Freivalds, R.: Complexity of Probabilistic Versus Deterministic Automata. In: Barzdins, J., Bjorner, D. (eds.) Baltic Computer Science. LNCS, vol. 502, pp. 565–613. Springer, Heidelberg (1991)
Ambainis, A., Freivalds, R.: 1-Way Quantum Finite Automata: Strengths, Weaknesses and Generalizations. In: FOCS, pp. 332–341 (1998)
Morita, K.: Reversible computing and cellular automata - A survey. Theoretical Computer Science 395(1), 101–131 (2008)
Buhrman, H., de Wolf, R.: Complexity Measures and Decision Tree Complexity: A Survey. Theoretical Computer Science 288(1), 21–43 (2002)
de Wolf, R.: Quantum Computing and Communication Complexity. University of Amsterdam (2001)
Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Kaye, R., Laflamme, R., Mosca, M.: An Introduction to Quantum Computing, Oxford (2007)
Ambainis, A.: Quantum query algorithms and lower bounds (survey article). In: Proceedings of FOTFS III, Trends on Logic, vol. 23, pp. 15–32 (2004)
Lace, L.: Doctoral Thesis. University of Latvia (2008)
Vasilieva, A.: Quantum Query Algorithms for AND and OR Boolean Functions, Logic and Theory of Algorithms. In: Proceedings of Fourth Conference on Computability in Europe, pp. 453–462 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vasilieva, A., Mischenko-Slatenkova, T. (2010). Quantum Query Algorithms for Conjunctions. In: Calude, C.S., Hagiya, M., Morita, K., Rozenberg, G., Timmis, J. (eds) Unconventional Computation. UC 2010. Lecture Notes in Computer Science, vol 6079. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13523-1_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-13523-1_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13522-4
Online ISBN: 978-3-642-13523-1
eBook Packages: Computer ScienceComputer Science (R0)