Enhancing Grover’s search algorithm: a modified approach to increase the probability of good states

Abstract

This article introduces an enhancement to the Grover search algorithm to speed up computing the probability of finding good states. It suggests incorporating a rotation phase angle determined mathematically from the derivative of the model during the initial iteration. At each iteration, a new phase angle is computed and used in a rotation gate around $y+z$ axis in the diffusion operator. The computed phase angles are optimized through an adaptive adjustment based on the estimated increasing ratio of the consecutive amplitudes. The findings indicate an average decrease of 28% in the required number of iterations resulting in a faster overall process and fewer number of quantum gates. For large search space, this improvement rises to 29.58%. Given the computational capabilities of the computer utilized for the simulation, the approach is applied to instances with up to 12 qubits or 4096 possible combination of search entries.