TITLE:
The Single-Rotation Quantum Search Algorithm: Amplitude Amplification with One Oracle Call
AUTHORS:
Ying Liu
KEYWORDS:
Quantum Computing, Grover’s Algorithm, Oracle, Amplitude Amplification, Quantum Circuits, Unitary Matrix, Single-Rotation Quantum Search
JOURNAL NAME:
Journal of Quantum Information Science,
Vol.16 No.2,
June
10,
2026
ABSTRACT: This paper presents the Single-Rotation Quantum Search Algorithm, which achieves amplitude-amplification with exactly one oracle call and one rotation operation. We prove that for unstructured search over N items, a single rotation by π/4 radians is both necessary and sufficient to amplify the marked state probability from 1/N to 1/2. This represents the theoretical minimum: no algorithm can succeed with fewer than one oracle call, and no additional rotations are needed beyond the single π/4 rotation. We provide explicit closed forms for the rotation operator with numerical values, demonstrating complete physical realizability. The algorithm is implemented by one oracle call, one diffusion call, and log(N) reflections. For N = 2n search spaces, the algorithm achieves success probability exactly 1/2 with one iteration, compared to O(
N
) iterations for Grover’s algorithm.