Abstract
We present general methods for proving lower bounds on the query complexity of nonadaptive quantum algorithms. Our results are based on the adversary method of Ambainis.
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
Aaronson, S.: Lower bounds for local search by quantum arguments. In: Proc. STOC 2004, pp. 465–474. ACM Press, New York (2004)
Aaronson, S., Shi, Y.: Quantum Lower Bounds for the Collision and the Element Distinctness Problems. Journal of the ACM 51(4), 595–605 (2004)
Ambainis, A.: Polynomial degree vs. quantum query complexity. J. Comput. Syst. Sci. 72(2), 220–238 (2006)
Bar-Yossef, Z., Kumar, R., Sivakumar, D.: Sampling Algorithms: lower bounds and applications. In: Proc. STOC 2001, pp. 266–275. ACM Press, New York (2001)
Beals, R., Buhrman, H., Cleve, R., Mosca, M., de Wolf, R.: Quantum lower bounds by polynomials. Journal of the ACM 48(4), 778–797 (2001)
Dürr, C., Heiligman, M., Høyer, P., Mhalla, M.: Quantum query complexity of some graph problems. SIAM J. Comput. 35(6), 1310–1328 (2006)
Friedl, K., Ivanyos, G., Magniez, F., Santha, M., Sen, P.: Hidden translation and orbit coset in quantum computing. In: STOC 2003: Proceedings of the thirty-fifth annual ACM symposium on Theory of computing (2003)
Grover, L.K., Radhakrishnan, J.: Quantum search for multiple items using parallel queries. arXiv (2004)
Hoyer, P., Spalek, R.: Lower bounds on quantum query complexity. EATCS Bulletin 87, 78–103 (2005)
Koiran, P., Nesme, V., Portier, N.: On the probabilistic query complexity of transitively symmetric problems, http://perso.ens-lyon.fr/pascal.koiran
Koiran, P., Nesme, V., Portier, N.: A quantum lower bound for the query complexity of Simon’s problem. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1287–1298. Springer, Heidelberg (2005)
Koiran, P., Nesme, V., Portier, N.: The quantum query complexity of abelian hidden subgroup problems. Theoretical Computer Science 380, 115–126 (2007)
Laplante, S., Magniez, F.: Lower bounds for randomized and quantum query complexity using Kolmogorov arguments. SIAM journal on Computing (to appear)
Nishimura, H., Yamakami, T.: An algorithmic argument for nonadaptive query complexity lower bounds on advised quantum computation (extended abstract). In: Fiala, J., Koubek, V., Kratochvíl, J. (eds.) MFCS 2004. LNCS, vol. 3153, pp. 827–838. Springer, Heidelberg (2004)
Rosenberg, A.L.: On the time required to check properties of graphs: A problem. SIGACT News, 15–16 (1973)
Simon, D.R.: On the power of quantum computation. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 116–123 (1994)
Spalek, R., Szegedy, M.: All quantum adversary methods are equivalent. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1299–1311. Springer, Heidelberg (2005)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Koiran, P., Landes, J., Portier, N., Yao, P. (2008). Adversary Lower Bounds for Nonadaptive Quantum Algorithms. In: Hodges, W., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2008. Lecture Notes in Computer Science(), vol 5110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69937-8_20
Download citation
DOI: https://doi.org/10.1007/978-3-540-69937-8_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69936-1
Online ISBN: 978-3-540-69937-8
eBook Packages: Computer ScienceComputer Science (R0)