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(
) iterations for Grover’s algorithm.
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