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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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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