Robust quantum algorithms with ε-biased oracles

Authors:
Tomoya Suzuki;Shigeru Yamashita;Masaki Nakanishi;Katsumasa Watanabe
Affiliations:
Graduate School of Information Science, Nara Institute of Science and Technology;Graduate School of Information Science, Nara Institute of Science and Technology;Graduate School of Information Science, Nara Institute of Science and Technology;Graduate School of Information Science, Nara Institute of Science and Technology
Venue:
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Year:
2006

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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.