Connectivity is a poor indicator of fast quantum search

David A. Meyer, Thomas G. Wong

Research output: Contribution to journalArticle

34 Scopus citations

Abstract

A randomly walking quantum particle evolving by Schrödinger's equation searches on d-dimensional cubic lattices in O(N) time when d≥5, and with progressively slower runtime as d decreases. This suggests that graph connectivity (including vertex, edge, algebraic, and normalized algebraic connectivities) is an indicator of fast quantum search, a belief supported by fast quantum search on complete graphs, strongly regular graphs, and hypercubes, all of which are highly connected. In this Letter, we show this intuition to be false by giving two examples of graphs for which the opposite holds true: one with low connectivity but fast search, and one with high connectivity but slow search. The second example is a novel two-stage quantum walk algorithm in which the walking rate must be adjusted to yield high search probability.

Original languageEnglish (US)
Article number110503
JournalPhysical Review Letters
Volume114
Issue number11
DOIs
StatePublished - Mar 18 2015

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All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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