Quantum walk search on Johnson graphs

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The Johnson graph J (n, k) is defined by n symbols, where vertices are kelement subsets of the symbols, and vertices are adjacent if they differ in exactly one symbol. In particular, J (n, 1) is the complete graph Kn, and J (n, 2) is the strongly regular triangular graph Tn, both of which are known to support fast spatial search by continuous-time quantum walk. In this paper, we prove that J (n, 3), which is the n-tetrahedral graph, also supports fast search. In the process, we show that a change of basis is needed for degenerate perturbation theory to accurately describe the dynamics. This method can also be applied to general Johnson graphs J (n, k) with fixed k.

Original languageEnglish (US)
Article number195303
JournalJournal of Physics A: Mathematical and Theoretical
Volume49
Issue number19
DOIs
StatePublished - Apr 12 2016
Externally publishedYes

Fingerprint

Quantum Walk
apexes
Graph in graph theory
set theory
perturbation theory
Complete Graph
Perturbation Theory
Continuous Time
Triangular
Adjacent
Subset

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

Quantum walk search on Johnson graphs. / Wong, Thomas.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 49, No. 19, 195303, 12.04.2016.

Research output: Contribution to journalArticle

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