As an unusual type of anomalous diffusion behavior, (transient) superballistic traort is not well understood but it has been experimentally observed recently. We here calculate the white noise effect (in Markov approximation) on the quantum diffusion in 1D tight-binding model with disordered and quasi-periodic region of size L attached to perfect lattices at both ends. Here we show the effect of white noise on spreading of the wave packet initially located at the center of the sublattice. We find threshold values of the white noise strength, beyond which the quantum hyperdiffusion does not occur. We predict from our numerical studies that the quantum hyperdiffusion exponent can be tuned by the strength of applied white noise. Therefore we can manually apply noise to a system to drive it to desired diffusion rate.
