Faster quantum walk search on a weighted graph

Thomas G. Wong

doi:10.1103/PhysRevA.92.032320

Faster quantum walk search on a weighted graph

Thomas G. Wong

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

A randomly walking quantum particle evolving by Schrödinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time Θ(N3/4). We give a weighted version of this graph that preserves vertex transitivity, and we show that the time to search on it can be reduced to nearly Θ(N). To prove this, we introduce two extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges and a method to determine how precisely the jumping rate of the quantum walk must be chosen.

Original language	English (US)
Article number	032320
Journal	Physical Review A - Atomic, Molecular, and Optical Physics
Volume	92
Issue number	3
DOIs	https://doi.org/10.1103/PhysRevA.92.032320
State	Published - Sep 21 2015
Externally published	Yes

All Science Journal Classification (ASJC) codes

Atomic and Molecular Physics, and Optics

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10.1103/PhysRevA.92.032320

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AB - A randomly walking quantum particle evolving by Schrödinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time Θ(N3/4). We give a weighted version of this graph that preserves vertex transitivity, and we show that the time to search on it can be reduced to nearly Θ(N). To prove this, we introduce two extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges and a method to determine how precisely the jumping rate of the quantum walk must be chosen.

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Faster quantum walk search on a weighted graph

Abstract

All Science Journal Classification (ASJC) codes

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