Abstract
We consider Grover’s unstructured search problem in the setting where each oracle call has some small probability of failing. We show that no quantum speed-up is possible in this case.
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
Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the ACM Symposium on the Theory of Computing, pp. 212–219 (1996)
Bennett, C.H., Bernstein, E., Brassard, G., Vazirani, U.: Strengths and weaknesses of quantum computing. SIAM J. Comput. 26(5), 1510–1523 (1997)
Boyer, M., Brassard, G., Høyer, P., Tapp, A.: Tight bounds on quantum searching. Fortschritte der Physik 46, 493–505 (1998)
Ambainis, A.: Quantum lower bounds by quantum arguments. In: Proceedings of the ACM Symposium on Theory of Computing, New York, pp. 636–643 (2000)
Ambainis, A.: Quantum search algorithms. SIGACT News 35(2), 22–35 (2004)
Harrow, A.: Personal communication (2006)
Shenvi, N., Brown, K.R., Whaley, K.B.: Effects of a random noisy oracle on search algorithm complexity. Phys. Rev. AÂ 68(5), 052313 (2003)
Knill, E., Laflamme, R., Zurek, W.H.: Resilient quantum computation. Science 279(5349), 342–345 (1998)
Long, G.L., Li, Y.S., Zhang, W.L., Tu, C.C.: Dominant gate imperfection in Grover’s quantum search algorithm. Physical Review A 61, 042305 (2000)
Shapira, D., Mozes, S., Biham, O.: Effect of unitary noise on Grover’s quantum search algorithm. Phys. Rev. A 67(4), 42301 (2003)
Brassard, G., Høyer, P., Mosca, M., Tapp, A.: Quantum amplitude amplification and estimation. In: Quantum computation and information. Contemp. Math, vol. 305, pp. 53–74. Amer. Math. Soc., Providence (2002)
Høyer, P., Mosca, M., de Wolf, R.: Quantum search on bounded-error inputs. In: Proceedings of ICALP 2003. LNCS, vol. 2719, pp. 291–299. Springer, Berlin (2003)
Buhrman, H., Newman, I., Röhrig, H., de Wolf, R.: Robust polynomials and quantum algorithms. Theory Comput. Syst. 40(4), 379–395 (2007); Preliminary version in STACS 2005
Iwama, K., Raymond, R., Yamashita, S.: General bounds for quantum biased oracles. IPSJ Journal 46(10), 1234–1243 (2005)
Suzuki, T., Yamashita, S., Nakanishi, M., Watanabe, K.: Robust quantum algorithms with ε-biased oracles. In: Chen, D.Z., Lee, D.T. (eds.) COCOON 2006. LNCS, vol. 4112, pp. 116–125. Springer, Heidelberg (2006)
Magniez, F., Nayak, A., Roland, J., Santha, M.: Search via quantum walk. In: Proceedings of the ACM Symposium on the Theory of Computing, New York, pp. 575–584 (2007)
Høyer, P., Lee, T., Špalek, R.: Negative weights make adversaries stronger. In: Proceedings of the ACM Symposium on the Theory of Computing, pp. 526–535 (2007) quant-ph/0611054
Beals, R., Buhrman, H., Cleve, R., Mosca, M., de Wolf, R.: Quantum lower bounds by polynomials. J. ACM 48(4), 778–797 (2001)
Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Kaye, P., Laflamme, R., Mosca, M.: An introduction to quantum computing. Oxford University Press, Oxford (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Regev, O., Schiff, L. (2008). Impossibility of a Quantum Speed-Up with a Faulty Oracle. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70575-8_63
Download citation
DOI: https://doi.org/10.1007/978-3-540-70575-8_63
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70574-1
Online ISBN: 978-3-540-70575-8
eBook Packages: Computer ScienceComputer Science (R0)