Advertisement

Quantum Query Algorithms for Conjunctions

  • Alina Vasilieva
  • Taisia Mischenko-Slatenkova
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6079)

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.

Keywords

Quantum computing query algorithm Boolean function algorithm design 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    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)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Grover, L.: A fast quantum mechanical algorithm for database search. In: Proceedings of 28th STOC 1996, pp. 212–219 (1996)Google Scholar
  3. 3.
    Calude, C.S.: Information and Randomness: an Algorithmic Perspective, 2nd edn. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  4. 4.
    Calude, C.S., Pavlov, B.: Coins, quantum measurements and Turing’s barrier. Quantum Information Processing 1(1-2), 107–127 (2002)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Calude, C.S., Stay, M.A.: Natural halting probabilities, partial randomness and zeta functions. Information and Computation 204(11), 1718–1739 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    Ambainis, A., Freivalds, R.: 1-Way Quantum Finite Automata: Strengths, Weaknesses and Generalizations. In: FOCS, pp. 332–341 (1998)Google Scholar
  8. 8.
    Morita, K.: Reversible computing and cellular automata - A survey. Theoretical Computer Science 395(1), 101–131 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Buhrman, H., de Wolf, R.: Complexity Measures and Decision Tree Complexity: A Survey. Theoretical Computer Science 288(1), 21–43 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    de Wolf, R.: Quantum Computing and Communication Complexity. University of Amsterdam (2001)Google Scholar
  11. 11.
    Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  12. 12.
    Kaye, R., Laflamme, R., Mosca, M.: An Introduction to Quantum Computing, Oxford (2007)Google Scholar
  13. 13.
    Ambainis, A.: Quantum query algorithms and lower bounds (survey article). In: Proceedings of FOTFS III, Trends on Logic, vol. 23, pp. 15–32 (2004)Google Scholar
  14. 14.
    Lace, L.: Doctoral Thesis. University of Latvia (2008)Google Scholar
  15. 15.
    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)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Alina Vasilieva
    • 1
  • Taisia Mischenko-Slatenkova
    • 1
  1. 1.Faculty of ComputingUniversity of LatviaRigaLatvia

Personalised recommendations