Research on phases of Grover-type algorithms

TL;DR

This paper investigates four phase-based improvements to Grover's algorithm, revealing they differ only by a global phase, enabling transfer of results among them and demonstrating their correctness with examples.

Contribution

The paper shows that four improved schemes of Grover's algorithm differ only by a global phase, simplifying analysis and application of these schemes.

Findings

All four schemes differ only by a global phase.

Results from one scheme can be extended to others.

Examples confirm the correctness of the schemes.

Abstract

When applying Grover's algorithm to an unordered database, the probability of obtaining correct results usually decreases as the quantity of target increases. To amend the limitation, numbers of improved schemes are proposed. In this paper, we focus on four improved schemes from phases, and find that they are just differed by a global phase. Based on this conclusion, the extensive researches on one scheme can be easily generated to other three schemes, and some examples are presented to indicate the correctness.