Oscillatory localization of quantum walks analyzed by classical electric circuits

Andris Ambainis, Krišjanis Prusis, Jevgenijs Vihrovs, Thomas G. Wong

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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
Issue number6
StatePublished - Dec 20 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics


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