The main results of our work is determining the differences between limiting properties in various models of quantum stochastic walks. In particular, we prove that in the case of strongly connected and a class of weakly connected directed graphs, local environment interaction evolution is relaxing, ...
(2007). Quantum walks on directed graphs, Quantum Information and Computation, 7, 93–102, quant-ph/0504116. MATH MathSciNet Google Scholar Moore, C., and Russell, A. (2001). Quantum walks on the hypercubes, quant-ph/0104137. Google Scholar Mülken, O. (2007). Inefficient quantum ...
Quantum walks on directed graphs.Preprint at https://arxiv.org/abs/quant-ph/0504116 (2005). Chandrashekar, C. M. & Busch, T. Quantum percolation and transition point of a directed discrete-time quantum walk. Sci. Rep. 4, 1–11. https://doi.org/10.1038/srep06583 (2014). Article ...
We set the ground for a theory of quantum walks on graphs- the generalization of random walks on finite graphs to the quantum world. Such quantum walks do not converge to any stationary distribution, as they are unitary and reversible. However, by suitably relaxing the definition, we can obta...
Random walks on graphs are a class of random walks widely used in the design and analysis of algorithms. Let G = (V,E) be an n-regular directed graph; that is, a graph where each vertex has n neighbors. Then we can label each edge with a number between 1 and n such that for ea...
Busch. Quantum percolation and transition point of a directed discrete-time quantum walk. Sci. Rep. 4, 6583 (2014). 37. B. Kollár, J. Novotný, T. Kiss & I. Jex. Discrete time quantum walks on percolation graphs. Eur. Phys. J. Plus 129(5), 103 (2014). 38. T. D. Mackay,...
We also discuss open challenges and future research directions relating to quantum walk on graphs in Section 6. 1.3 Comparison with other surveys There have been related attempts and literature surveys in the past on quantum walks, with their advantages and limitations. In this subsection, we overv...
A. Glos, J.A. Miszczak, M. Ostaszewski, Limiting properties of stochastic quantum walks on directed graphs. J. Phys. A Math. Theor.51(3), 035304 (2017) ArticleADSMathSciNetGoogle Scholar M. Asano, M. Ohya, Y. Tanaka, A. Khrennikov, I. Basieva, On application of Gorini-Kossakow...
The generalised model allows also the introduction of directed edges between two already existing nodes. In this work we study the quantum (and classical) Page Rank algorithm on graphs created with this model as implemented in NetworkX40. Let us now discuss results from the application of the ...
The earliest work on quantum walks on graphs with broken links is, to our knowledge, by Romanelli et al. [40]. They investigated the one-dimensional discrete time Hadamard quantum walk on the line under the decoherence effect of dynamical percolation (broken links). Their model has a single ...