TITLE:
Grover’s Model with Single Oracle Call and Log(N) Different Diffusion Calls
AUTHORS:
Ying Liu
KEYWORDS:
Quantum Computing, Grover’s Algorithm, Oracle, Amplitude Amplification, Quantum Circuits, Unitary Matrix, Single-Iteration Quantum Search, Single-Rotation Quantum Search
JOURNAL NAME:
Journal of Quantum Information Science,
Vol.16 No.2,
June
22,
2026
ABSTRACT: The author has recently presented the Single-Iteration Quantum Search Algorithm, which achieves amplitude-amplification with exactly one oracle call and one π/4 rotation [1]. For N = 2n search spaces, the algorithm achieves success probability exactly 1/2 with one iteration of oracle operator and one π/4 rotation with log(N) different diffusion calls, compared to O(
N
) iterations (O(
N
) oracle calls and O(
N
) same diffusion calls) for Grover’s algorithm. This work presents a simpler and cleaner derivation for one oracle call and log(N) diffusion calls, while the original proof was based on Cartan-Dieudonné theorem [1]. The standard lower bounds for unstructured quantum search still apply even though the number of oracle calls is reduced from O(
N
) to O(1) and the number of diffusion calls is reduced from O(
N
) to O(logN).