We analyze continuous-time quantum and classical random walk on spidernet lattices. In the framework of Stieltjes transform, we obtain density of states, which is an efficiency measure for the performance of classical and quantum mechanical transport processes on graphs, and calculate the spacetime transition probabilities between two vertices of the lattice. Then we analytically show that ther...

Demosthenes Ellinas † and Ioannis Smyrnakis ‡ Technical University of Crete, Department of Sciences Division of Mathematics, GR 731 00, Chania, Greece. e-mail: † [email protected] ‡ [email protected] Abstract Rules for quantizing the walker+coin parts of a classical random walk are provided by treating them as interacting quantum systems. A quantum optical random walk (QORW), is introduc...

We look at two possible routes to classical behavior for the discrete quantum random walk on the line: decoherence in the quantum “coin” which drives the walk, or the use of higher-dimensional coins to dilute the effects of interference. We use the position variance as an indicator of classical behavior, and find analytical expressions for this in the long-time limit; we see that the multicoin ...

For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus, propagates at a rate which is linear in time, as compared to the square root rate for a classical random walk. Indeed, it has been suggested that there are gra...

In quantum systems, one usually seeks to minimize dephasing noise and disorder. The efficiency of transport in a quantum system is usually degraded by the presence of noise and disorder. However, it has been shown that the combination of the two can lead to significantly more efficiency than each by itself. Here, we consider how the addition of nonlocal noise, in the form of incoherent hopping,...

We show that the hitting time of the discrete time quantum random walk on the n-bit hypercube from one corner to its opposite is polynomial in n. This gives the first exponential quantum-classical gap in the hitting time of discrete quantum random walks. We provide the framework for quantum hitting time and give two alternative definitions to set the ground for its study on general graphs. We t...

We introduce a discrete–time quantum walk on a one-dimensional momentum space including both discrete jumps and continuous drift. Its time evolution has two different stages. Initially a Markovian diffusion develops during a characteristic time interval, after which dynamical localization sets in, as in the well known Quantum Kicked Rotor system. For some exceptional values of the model’s param...