As an application, we introduce three types of quantum graph walks, and treat their relation.doi:10.48550/arXiv.1211.4719Yusuke HiguchiNorio KonnoIwao SatoEtsuo SegawaMathematicsHiguchi, Yu., Konno, N., Sato, I., Segawa, E.: Quantum graph walks II: quantum walks on graph coverings, Yokohama ...
We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. In the case when the marked setconsists of a single vertex, the number of steps of the quantum walk is quadratically smaller than the classical hitting timeof any reversible...
We address continuous-time quantum walks on graphs, and discuss whether and how quantum-limited measurements on the walker may extract information on the tunnelling amplitude between the nodes of the graphs. For a few remarkable families of graphs, we evaluate the ultimate quantum bound to precision...
Quantum walks have been employed widely to develop new tools for quantum information processing recently. A natural quantum walk dynamics of interacting particles can be used to implement efficiently the universal quantum computation. In this work quantum walks of electrons on a graph are studied. ...
Torsello and L. Rossi. A quantum Jensen-Shannon graph kernel using the continuous-time quantum walk. In Proceedings of International Workshop on Graph-Based Representations in Pattern Recognition (GbRPR), 2013, pp. 121-131.A Quantum Jensen-Shannon Graph Kernel Using the Continuous-Time Quantum ...
1 2 1. EIGENVALUES AND THE LAPLACIAN OF A GRAPH From the start, spectral graph theory has had applications to chemistry [27]. Eigenvalues were associated with the stability of molecules. Also, graph spectra arise naturally in various problems of theoretical physics and quantum mechanics, for ...
A continuous-time quantum walk is modelled using a graph. In this short paper, we provide lower bounds on the size of a graph that would allow for some quantum phenomena to occur. Among other things, we show that, in the adjacency matrix quantum walk model, the number of edges is ...
Continuous-time quantum walks on a cycle graph. Phys. Rev. A 73, 012313 (2006).Dmitry Solenov and Leonid Fedichkin. Continuous-time quantum walks on a cycle graph. Phys. Rev. A, 73:012313, 2006.D. Solenov, L. Fredichkin, Continuous-time quantum walks on a cycle graph, Phys. Rev...
Quantum PhysicsThis paper has been withdrawn by the authors; replaced by arXiv:0705.2531v2 [quant-ph].doi:10.48550/arXiv.quant-ph/0701033J. B. WangB. L. DouglasPhysicsWang, J. B., and Douglas, B. L. (2007). Graph identification by quantum walks, quant-ph/0701033....
Networks—or graphs—are universal descriptors of systems of interacting elements. In biomedicine and healthcare, they can represent, for example, molecular interactions, signalling pathways, disease co-morbidities or healthcare systems. In this Perspective, we posit that representation learning can realiz...