Simplified Quantum Algorithm for the Oracle Identification Problem

TL;DR

This paper presents a simplified quantum algorithm for the oracle identification problem, achieving near-optimal query complexity with a more elegant proof compared to prior work.

Contribution

It offers a simpler, more elegant proof for a quantum query algorithm that matches the best known complexity bounds for the oracle identification problem.

Findings

Quantum query complexity is $O(\sqrt{rac{n\log M}{\log(n/\log M)+1}})$.

The paper provides a simpler proof of existing bounds from Kothari 2014.

The algorithm improves understanding of quantum query efficiency for set identification.

Abstract

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.