Abstract : In this talk, I will introduce the tailed model of quantum walks and some of its interesting results. Quantum walk is the quantum analogy of random walk. Unlike the usual quantum walks, the tailed model guarantees the convergence of the state of the walker to a stationary state. We are interested in utilizing this converging property. We consider the Grover dynamics with a specific initial state and we obtain the scattering of the dynamics in the long run. Based on the scattering matrix, we obtain a characterization of bipartite graphs. Moreover, we show that, if the underlying graph is (non-)bipartite, the stationary state expresses a (pseudo-)current function which satisfies (pseudo-)Kirchhoff laws. Furthermore, we introduce a quantum analogy of the electrical energy, called ‘comfortability’ and we show that the comfortability of the underlying graph can be expressed in terms of the geometric properties of the graph.
web page https://arxiv.org/abs/2002.05261
When: 29th November, 2022
Where: Luminy, room 04.05 of building TPR2. CaNa seminar.
On Zoom : https://univ-amu-fr.zoom.us/j/85935457975?pwd=aEZhb3NLQjRLTjkwZkJxRHRUOEtaZz09