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Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., et al. (1995) Elementary Gates for Quantum Computation. Physical Review A, 52, 3457-3467.
https://doi.org/10.1103/physreva.52.3457

has been cited by the following article:

• 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).