Quantum Search Algorithm for Set Operation

TL;DR

This paper introduces a quantum algorithm for set intersection that significantly reduces computational complexity compared to classical methods, utilizing Grover's algorithm combined with classical memory and iteration.

Contribution

The paper presents a novel quantum algorithm for set intersection with a complexity of sqrt(|A|*|B|*|C|), improving over classical approaches.

Findings

Quantum set intersection algorithm with sqrt complexity

Combination of Grover's algorithm and classical methods

Potential application to other set operations

Abstract

The operations of data set, such as intersection, union and complement, are the fundamental calculation in mathematics. It's very significant that designing fast algorithm for set operation. In this paper, the quantum algorithm for intersection is presented. And its running time is sqrt(|A|*|B|*|C|) for set operation C = A intersection B, while classical computation needs O (|A| *|B|) steps of computation in general, where |.| denotes the size of set. The presented algorithm is the combination of Grover's algorithm, classical memory and classical iterative computation, and the combination method decrease the complexity of designing quantum algorithm.The method can be used to design other set operations also. Keywords: Set operation, General Grover iteration, Grover's algorithm