Abstract
K. Iwama and R. Freivalds considered query algorithms where the black box contains a permutation. Since then several authors have compared quantum and deterministic query algorithms for permutations. It turns out that the case of \(n\)-permutations where \(n\) is an odd number is difficult. There was no example of a permutation problem where quantization can save half of the queries for \((2m+1)\)-permutations if \(m\ge 2\). Even for \((2m)\)-permutations with \(m\ge 2\), the best proved advantage of quantum query algorithms is the result by Iwama/Freivalds where the quantum query complexity is \(m\) but the deterministic query complexity is \((2m-1)\). We present a group of \(5\)-permutations such that the deterministic query complexity is 4 and the quantum query complexity is 2.
The research was supported by the project ERAF Nr.2DP/2.1.1.1/13/APIA/ VIAA/027.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Ablayev, F.M., Freivalds, R.: Why sometimes probabilistic algorithms can be more effective. In: Gruska, J., Rovan, B., Wiedermann, J. (eds.) MPCS 1986. LNCS, vol. 233, pp. 1–14. Springer, Heidelberg (1986)
Ambainis, A.: Quantum lower bounds by quantum arguments. J. Comput. Syst. Sci. 64(4), 750–767 (2002)
Ambainis, A.: Polynomial degree vs. quantum query complexity. In: Proceedings of FOCS 1998, pp. 230–240 (1998)
Ambainis, A., Freivalds, R.: 1-way quantum finite automata: strengths, weaknesses and generalizations. In: Proceedings of FOCS 1998, pp. 332– 341. Also quant-ph/9802062
Ambainis, A., de Wolf, R.: Average-case quantum query complexity. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 133–144. Springer, Heidelberg (2000)
Buhrman, H., de Wolf, R.: Complexity measures and decision tree complexity: a survey. Theoret. Comput. Sci. 288(1), 21–43 (2002)
Beals, R., Buhrman, H., Cleve, R., Mosca, M., de Wolf, R.: Quantum lower bounds by polynomials. J. ACM 48(4), 778–797 (2001)
Buhrman, H., Cleve, R., de Wolf, R., Zalka, C.: Bounds for small-error and zero-error quantum algorithms. In: Proceedings of FOCS 1999, pp. 358–368 (1999)
Cleve, R., Ekert, A., Macchiavello, C., Mosca, M.: Quantum algorithms revisited. Proc. R. Soc. Lond. A 454, 339–354 (1998)
Deutsch, D., Jozsa, R.: Rapid solutions of problems by quantum computation. Proc. R. Soc. Lond. A 439, 553 (1992)
Freivalds, R.: Languages recognizable by quantum finite automata. In: Farré, J., Litovsky, I., Schmitz, S. (eds.) CIAA 2005. LNCS, vol. 3845, pp. 1–14. Springer, Heidelberg (2006)
Freivalds, R., Iwama, K.: Quantum queries on permutations with a promise. In: Maneth, S. (ed.) CIAA 2009. LNCS, vol. 5642, pp. 208–216. Springer, Heidelberg (2009)
Simon, I.: String matching algorithms and automata. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814, pp. 386–395. Springer, Heidelberg (1994)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Mischenko-Slatenkova, T., Vasilieva, A., Kucevalovs, I., Freivalds, R. (2015). Quantum Queries on Permutations. In: Shallit, J., Okhotin, A. (eds) Descriptional Complexity of Formal Systems. DCFS 2015. Lecture Notes in Computer Science(), vol 9118. Springer, Cham. https://doi.org/10.1007/978-3-319-19225-3_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-19225-3_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19224-6
Online ISBN: 978-3-319-19225-3
eBook Packages: Computer ScienceComputer Science (R0)