2024/06/19 by Alok Shukla, Shukla, Alok, Prakash Vedula +1
Computer Science · #81P15 #81P45 #81P68 #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2406.13785
openalex publication_date 2024/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper presents an enhancement to Grover's search algorithm for instances where the number of items (or the size of the search problem) N is not a power of 2. By employing an efficient algorithm for the preparation of uniform quantum superposition states over a subset of the computational basis states, we demonstrate that a considerable reduction in the number of oracle calls (and Grover's iterations) can be achieved in many cases. For special cases (i.e., when N is of the form such that it is slightly greater than an integer power of 2), the reduction in the number of oracle calls (and Grover's iterations) asymptotically approaches 29.33%. This improvement is significant compared to the traditional Grover's algorithm, which handles such cases by rounding N up to the nearest power of 2. The key to this improvement is our algorithm for the preparation of uniform quantum superposition states over a subset of the computational basis states, which requires gate complexity and circuit depth of only O (log2 (N)) , without using any ancilla qubits.