TY - JOUR

T1 - Oscillatory localization of quantum walks analyzed by classical electric circuits

AU - Ambainis, Andris

AU - Prusis, Krišjanis

AU - Vihrovs, Jevgenijs

AU - Wong, Thomas G.

N1 - Publisher Copyright:
© 2016 American Physical Society.

PY - 2016/12/20

Y1 - 2016/12/20

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevA.94.062324

DO - 10.1103/PhysRevA.94.062324

M3 - Article

AN - SCOPUS:85007090201

VL - 94

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 6

M1 - 062324

ER -