Oscillatory localization of quantum walks analyzed by classical electric circuits

Andris Ambainis, Krišjanis Prusis, Jevgenijs Vihrovs, Thomas Wong

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Article number062324
JournalPhysical Review A
Volume94
Issue number6
DOIs
StatePublished - Dec 20 2016
Externally publishedYes

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dissipation
electric networks
apexes
projection

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

Cite this

Oscillatory localization of quantum walks analyzed by classical electric circuits. / Ambainis, Andris; Prusis, Krišjanis; Vihrovs, Jevgenijs; Wong, Thomas.

In: Physical Review A, Vol. 94, No. 6, 062324, 20.12.2016.

Research output: Contribution to journalArticle

Ambainis, Andris ; Prusis, Krišjanis ; Vihrovs, Jevgenijs ; Wong, Thomas. / Oscillatory localization of quantum walks analyzed by classical electric circuits. In: Physical Review A. 2016 ; Vol. 94, No. 6.
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