Simplified Quantum Algorithm for the Oracle Identification Problem

• URL: http://arxiv.org/abs/2109.03902v1
• Date: Wed, 8 Sep 2021 19:48:27 GMT
• Title: Simplified Quantum Algorithm for the Oracle Identification Problem
• Authors: Leila Taghavi
• Abstract summary: oracle access to bits of an unknown string $x$ of length $n$, with the promise that it belongs to a known set $Csubseteq0,1n$. 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 $Oleft(sqrtfracnlog M log(n/log M)+1right)$, where $M$ is the size of $C$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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