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, sigma(t) scales as sigma(t)similar tot, unlike the classical random walk for which sigma(t)similar toroott. 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 Tsimilar toalpha(-2), where alpha is the standard deviation of the noise

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa