2025/09/24 by Christopher Cardullo, Cardullo, Christopher, Min Kyu Kang +1
Computer Science · Mathematics · #68Q12 #68Q99 #68W01 #81P68 #90C15 #Amplitude #Approximation algorithm #FOS: Mathematics #FOS: Physical sciences #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms #Numerical methods in inverse problems #Optimal control #Optimization and Control (math.OC) #Phase (matter) #Point (geometry) #Point target #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2509.20610
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the generalized Grover's algorithm with an arbitrary amplitude vector to find the optimal phase change for maximizing the gain in probability for the target of each iteration. In the classic setting of Grover's algorithm with a real initial amplitude vector, we find that a phase change of π stays optimal until the probability of observing the target is quite close to 1. We provide a formula for identifying this cut-off point based on the size of the data set. When the amplitude is truly complex, we find that the optimal phase change depends non-trivially on the complexity of the amplitude vector. We provide an optimization formula to identify the required optimal phase change.