Grover's Algorithm Extensions - A Systematic Literature Review

Quantum computing has emerged as a transformative field, offering superior computational capabilities over its classical counterparts in solving complex problems. Among the most well-known quantum algorithms is Grover?s algorithm, which was introduced as a quantum search algorithm in an unstructured database. It achieves quadratic speedup, requiring only O(?N) queries compared to the classical O(N), making it highly relevant for the information-processing. Despite its strengths, Grover?s algorithm is widely recognized to have been limited, depending on its intended utilization, prompting numerous perceptive improvement extensions were born. The goal of this study was to identify established Grover?s algorithm extensions through a systematic literature review. Indexed article items published between 2019 and 2025 were selected from different sources, based on specific defined keywords. The review classififies extensions into three primary aspects, time-complexity, optimization and quantum cost, including their bi-combinations and tri-combinations. Additionally, a conceptual framework is proposed to summarize these contributions and serve as guidance for future research. The findings highlight how the extensions address performance challenges and expand the applicability of Grover?s algorithm across different domain applications. This review not only provides a clearer and establishes a foundation for future developments in quantum search algorithms and their broader utilization in quantum computing applications.