One-dimensional quantum walk with unitary noise

The effect of unitary noise on the discrete one-dimensional quantum walk is studied using computer simulations. For the noiseless quantum walk, starting at the origin (n=0) at time t=0, the position distribution P_t(n) at time t is very different from the Gaussian distribution obtained for the classical random walk. Furthermore, its standard deviation, σ(t) scales as σ(t)∼t, unlike the classical random walk for which σ(t)∼√t. It is shown that when the quantum walk is exposed to unitary noise, it exhibits a crossover from quantum behavior for short times to classical-like behavior for long times. The crossover time is found to be T∼α^-2, where α is the standard deviation of the noise.