Convergence properties of fixed-point search with general but equal phase shifts for any iterations

TL;DR

This paper analyzes the convergence behavior of a generalized fixed-point quantum search algorithm that uses equal phase shifts, extending Grover's original approach with phase shifts of π/3.

Contribution

It provides a theoretical investigation into the convergence properties of fixed-point search algorithms with arbitrary equal phase shifts for any number of iterations.

Findings

Convergence behavior depends on the choice of phase shifts.

General phase shifts can optimize the search process.

Theoretical insights into the stability of fixed-point quantum search.

Abstract

Grover presented the fixed-point search by replacing the selective inversions by selective phase shifts of $\pi /3$. In this paper, we investigate the convergence behavior of the fixed-point search algorithm with general but equal phase shifts for any iterations.