Two-dimensional Quantum Random Walk

Two-dimensional quantum random walk

We analyze several families of two-dimensional quantum random walks. The feasible region (the region where probabilities do not decay exponentially with time) grows linearly with time, as is the case with one-dimensional QRW. The limiting shape of the feasible region is, however, quite different. The limit region turns out to be an algebraic set, which we characterize as the rational image of a...

Two-site Quantum Random Walk

We study the measure theory of a two-site quantum random walk. The truncated decoherence functional defines a quantum measure μn on the space of n-paths, and the μn in turn induce a quantum measure μ on the cylinder sets within the space Ω of untruncated paths. Although μ cannot be extended to a continuous quantum measure on the full σ-algebra generated by the cylinder sets, an important questi...

Random walk on a two-dimensional random environment

Quantum Random Walk via Classical Random Walk With Internal States

In recent years quantum random walks have garnered much interest among quantum information researchers. Part of the reason is the prospect that many hard problems can be solved efficiently by employing algorithms based on quantum random walks, in the same way that classical random walks have played a central role in many hugely successful randomized algorithms. In this paper we introduce a new ...

On two-dimensional random walk among heavy-tailed conductances

We consider a random walk among unbounded random conductances on the two-dimensional integer lattice. When the distribution of the conductances has an infinite expectation and a polynomial tail, we show that the scaling limit of this process is the fractional kinetics process. This extends the results of the paper [BČ10] where a similar limit statement was proved in dimension d ≥ 3. To make thi...