Grover search with smaller oracles

TL;DR

This paper introduces a modified Grover search algorithm that uses smaller oracles for conditions expressed as intersections, resulting in reduced time complexity compared to the original Grover search.

Contribution

It presents a novel Grover search method utilizing smaller oracles for intersecting conditions, improving efficiency over traditional approaches.

Findings

Reduced time complexity compared to original Grover search

Effective for search conditions expressed as intersections of sets

Demonstrates practical efficiency improvements

Abstract

Grover search is one of the most important quantum algorithms. In this paper, we consider a kind of search that the conditions of satisfaction $T$ can be rewritten as $T=T_1\bigcap T_2$. Then we present a new Grover search with smaller oracles. The time complexity of this algorithm $O(\frac{\pi}{4}\sqrt{\frac{N}{b\lambda}}+\frac{\pi}{4}\sqrt{\frac{b}{\tau}})$, which is smaller than the time complexity of original Grover search, i.e. $O(\frac{\pi}{4}\sqrt{\frac{N}{M}})$.