Abstract
This paper considers the quantum query complexity of ε-biased oracles that return the correct value with probability only 1/2 + ε. In particular, we show a quantum algorithm to compute N-bit OR functions with \(O(\sqrt{N}/{\varepsilon})\) queries to ε-biased oracles. This improves the known upper bound of \(O(\sqrt{N}/{\varepsilon}^2)\) and matches the known lower bound; we answer the conjecture raised by the paper [1] affirmatively. We also show a quantum algorithm to cope with the situation in which we have no knowledge about the value of ε. This contrasts with the corresponding classical situation, where it is almost hopeless to achieve more than a constant success probability without knowing the value of ε.
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Iwama, K., Raymond, R., Yamashita, S.: General bounds for quantum biased oracles. IPSJ Journal 46(10), 1234–1243 (2005)
Shor, P.W.: An algorithm for quantum computation: discrete log and factoring. In: Proc. 35th Annual IEEE Symposium on Foudations of Computer Science, pp. 124–134 (1994)
Grover, L.K.: A fast quantum mechanical algorithm for database search. In: STOC, pp. 212–219 (1996)
Ambainis, A.: Quantum lower bounds by quantum arguments. J. Comput. Syst. Sci. 64(4), 750–767 (2002)
Beals, R., Buhrman, H., Cleve, R., Mosca, M., de Wolf, R.: Quantum lower bounds by polynomials. In: Proc. 39th Annual IEEE Symposium on Foudations of Computer Science, pp. 352–361 (1998)
Boyer, M., Brassard, G., Høyer, P., Tapp, A.: Tight bounds on quantum searching. In: Proc. of the Workshop on Physics of Computation: PhysComp 1996, LANL preprint (1996), http://xxx.lanl.gov/archive/quant-ph/9605034
Feige, U., Raghavan, P., Peleg, D., Upfal, E.: Computing with Noisy Information. SIAM J. Comput. 23(5), 1001–1018 (1994)
Høyer, P., Mosca, M., de Wolf, R.: Quantum search on bounded-error inputs. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 291–299. Springer, Heidelberg (2003)
Buhrman, H., Newman, I., Röhrig, H., de Wolf, R.: Robust polynomials and quantum algorithms. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 593–604. Springer, Heidelberg (2005)
Adcock, M., Cleve, R.: A quantum Goldreich-Levin Theorem with cryptographic applications. In: Alt, H., Ferreira, A. (eds.) STACS 2002. LNCS, vol. 2285, pp. 323–334. Springer, Heidelberg (2002)
Brassard, G., Høyer, P., Mosca, M., Tapp, A.: Quantum amplitude amplification and estimation. In: Quantum Computation & Information. AMS Contemporary Mathematics Series Millenium Volume, vol. 305, pp. 53–74 (2002)
Suzuki, T., Yamashita, S., Nakanishi, M., Watanabe, K.: Robust quantum algorithms with ε-biased oracles. Technical Report LANL preprint (2006), http://xxx.lanl.gov/archive/quant-ph/0605077
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Suzuki, T., Yamashita, S., Nakanishi, M., Watanabe, K. (2006). Robust Quantum Algorithms with ε-Biased Oracles. In: Chen, D.Z., Lee, D.T. (eds) Computing and Combinatorics. COCOON 2006. Lecture Notes in Computer Science, vol 4112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11809678_14
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DOI: https://doi.org/10.1007/11809678_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-36925-7
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