Robust Quantum Algorithms for Oracle Identification (Theoretical Computer Science and its Applications)
Kazuo Iwama, Akinori Kawachi, Rudy Raymond, Shigeru Yamashita · Institutional Repositories DataBase (IRDB) · 2005
The oracle identification problem (OIP) was introduced by Ambainis et.al. [4], which is given as a set $S$ of $M$ oracles and a hidden oracle $f$ .Our task is to figure out which oracle in $S$ is equal to the hidden $f$ by doing queries to $f$ .OIP includes several problems such as Grover Search as special cases.In this paper, we design robust algorithms, i.e., those which are tolerant against noisy oracles, for OIP.Our results include: (i) For any oracle set $S$ such that $|S|$ is polynomial in $N$ , $O(\sqrt{N})$ queries are enough to identify the hidden oracle, which is obviously optimal since this OIP includes Grover Search as a special case, (ii) For the case that $|S|\leq 2^{N^{d}}(d<1)$ , we design an algorithm whose query complexity is $O(\sqrt{N\log M/\log N})$ and matches the lower bound proved in [4].(Hi) We can furthermore design a robust algorithm whose complexity changes smoothly between the complexity of (ii) and the complexity of recovering all information about the hidden oracle whose complexity is $O(N)$ as showed by Buhrman et.al. in [11].Thus our new algorithms are not only robust but also their query complexities are even better than the previous noiseless case [4],