Southwest Quantum Information and Technology

Oscillatory localization of quantum walks

Presenting Author: Thomas Wong, University of Texas at Austin

We examine an unexplored quantum phenomenon we call oscillatory localization, where a discrete-time quantum walk with Grover's diffusion coin jumps back and forth between two vertices. We then connect it to the power dissipation of a related electric network. Namely, we show that there are only two kinds of oscillating states, called uniform states and flip states, and that the projection of an arbitrary state onto a flip state is bounded by the power dissipation of an electric circuit. By applying this framework to states along a single edge of a graph, we show that low effective resistance implies oscillatory localization of the quantum walk. This reveals that oscillatory localization occurs on a large variety of regular graphs, including edge-transitive, expander, and high-degree graphs. As a corollary, high edge connectivity also implies localization of these states, since it is closely related to electric resistance.

Read this article online: http://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.062324

(Session 5 : Thursday from 5:00pm - 7:00pm)