Abstract
The oracle identification problem (OIP) was introduced by Ambainis et al. [3]. It is given as a set S of M oracles and a blackbox oracle f. Our task is to figure out which oracle in S is equal to the blackbox f by making queries to f. OIP includes several problems such as the Grover Search as special cases. In this paper, we improve the algorithms in [3] by providing a mostly optimal upper bound of query complexity for this problem: (i) For any oracle set S such that \(|S| \le 2^{N^d}\) (d < 1), we design an algorithm whose query complexity is \(O(\sqrt{N\log{M}/\log{N}})\), matching the lower bound proved in [3]. (ii) Our algorithm also works for the range between \(2^{N^d}\) and 2N/logN (where the bound becomes O(N)), but the gap between the upper and lower bounds worsens gradually. (iii) Our algorithm is robust, namely, it exhibits the same performance (up to a constant factor) against the noisy oracles as also shown in the literatures [2, 11, 18] for special cases of OIP.
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Ambainis, A., Iwama, K., Kawachi, A., Raymond, R., Yamashita, S. (2006). Improved Algorithms for Quantum Identification of Boolean Oracles. In: Arge, L., Freivalds, R. (eds) Algorithm Theory – SWAT 2006. SWAT 2006. Lecture Notes in Computer Science, vol 4059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11785293_27
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DOI: https://doi.org/10.1007/11785293_27
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