Simplified Quantum Algorithm for the Oracle Identification Problem
This is an incremental improvement for researchers in quantum computing, offering a more elegant derivation of an existing result.
The paper tackles the oracle identification problem by developing a quantum query algorithm with query complexity O(√(n log M / (log(n/log M) + 1))), matching a known bound from prior work but providing a simpler proof.
In the oracle identification problem we have oracle access to bits of an unknown string $x$ of length $n$, with the promise that it belongs to a known set $C\subseteq\{0,1\}^n$. The goal is to identify $x$ using as few queries to the oracle as possible. We develop a quantum query algorithm for this problem with query complexity $O\left(\sqrt{\frac{n\log M }{\log(n/\log M)+1}}\right)$, where $M$ is the size of $C$. This bound is already derived by Kothari in 2014, for which we provide a more elegant simpler proof.