We show that constant-depth polynomial-size exact quantum circuits with unbounded fan-out gates,called QNCof circuits,are powerful.More concretely,we first show that there exists a QNCof circuit for the OR function.This is an affirmative answer to the question of Hoyer and Spalek.Then,we show that,under a plausible assumption,there exists a classically hard problem that is solvable by a QNCof circuit with gates for the quantum Fourier transform.