Robust Quantum Algorithms for Oracle Identification

The oracle identification problem (OIP) was introduced by Ambainis et al. [4]. 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 [4] by providing a mostly optimal upper bound of query complexity for this problem: (i) For any oracle set S such that |S| ≤ 2Nd (d < 1), we design an algorithm whose query complexity is O( √ N logM/ logN), matching the lower bound proved in [4]. (ii) Our algorithm also works for the range between 2 d and 2 log N (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, 12, 21] for special cases of OIP. keywords: quantum computing, query complexity and algorithmic learning theory