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We analyze continuous-time quantum walks on necklace graphs - cyclical graphs consisting of many copies of a smaller graph (pearl). Using a Bloch-type ansatz for the eigenfunctions, we block-diagonalize the Hamiltonian, reducing the effective size of the problem to the size of a single pearl. We then present a general approach for showing that the mixing time scales (with growing size of the necklace) similarly to that of a simple walk on a cycle. Finally, we present results for mixing on several necklace graphs.
We compare discrete-time quantum walks on graphs to their natural classical equivalents, which we argue are lifted Markov chains, that is, classical Markov chains with added memory. We show that these can simulate quantum walks, allowing us to answer
We consider the Grover walk on infinite trees from the view point of spectral analysis. From the previous works, infinite regular trees provide localization. In this paper, we give the complete characterization of the eigenspace of this Grover walk,
This volume contains a selection of papers presented at the 9th in a series of international conferences on Quantum Simulation and Quantum Walks (QSQW). During this event, we worked on the development of theories based upon quantum walks and quantum
We consider quantum random walks on congested lattices and contrast them to classical random walks. Congestion is modelled with lattices that contain static defects which reverse the walkers direction. We implement a dephasing process after each step
It was recently pointed out that identifiability of quantum random walks and hidden Markov processes underlie the same principles. This analogy immediately raises questions on the existence of hidden states also in quantum random walks and their rela