Global symmetry is unnecessary for fast quantum search

Jonatan Janmark, David A. Meyer, Thomas Wong

Research output: Contribution to journalArticle

32 Citations (Scopus)

Abstract

Grover's quantum search algorithm can be formulated as a quantum particle randomly walking on the (highly symmetric) complete graph, with one vertex marked by a nonzero potential. From an initial equal superposition, the state evolves in a two-dimensional subspace. Strongly regular graphs have a local symmetry that ensures that the state evolves in a three-dimensional subspace but most have no global symmetry. Using degenerate perturbation theory, we show that quantum random walk search on known families of strongly regular graphs, nevertheless, achieves the full quantum speed-up of Θ(N), disproving the intuition that fast quantum search requires global symmetry.

Original languageEnglish (US)
Article number210502
JournalPhysical Review Letters
Volume112
Issue number21
DOIs
StatePublished - May 28 2014
Externally publishedYes

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symmetry
walking
random walk
apexes
perturbation theory

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

Global symmetry is unnecessary for fast quantum search. / Janmark, Jonatan; Meyer, David A.; Wong, Thomas.

In: Physical Review Letters, Vol. 112, No. 21, 210502, 28.05.2014.

Research output: Contribution to journalArticle

Janmark, Jonatan ; Meyer, David A. ; Wong, Thomas. / Global symmetry is unnecessary for fast quantum search. In: Physical Review Letters. 2014 ; Vol. 112, No. 21.
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