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Global Symmetry is Unnecessary for Fast Quantum Search
KTH, School of Engineering Sciences (SCI), Physics.
2014 (English)In: Physical Review Letters, ISSN 0031-9007, Vol. 112, no 21, 210502- p.Article in journal (Refereed) Published
Abstract [en]

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 Theta(root N), disproving the intuition that fast quantum search requires global symmetry.

Place, publisher, year, edition, pages
2014. Vol. 112, no 21, 210502- p.
National Category
Physical Sciences
URN: urn:nbn:se:kth:diva-147422DOI: 10.1103/PhysRevLett.112.210502ISI: 000336765200003ScopusID: 2-s2.0-84901675814OAI: diva2:731178

QC 20140701

Available from: 2014-07-01 Created: 2014-06-27 Last updated: 2014-07-01Bibliographically approved

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