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Quantum Information Processing

, Volume 14, Issue 6, pp 1767–1775 | Cite as

Diagrammatic approach to quantum search

  • Thomas G. Wong
Article

Abstract

We introduce a simple diagrammatic approach for estimating how a randomly walking quantum particle searches on a graph in continuous time, which involves sketching small weighted graphs with self-loops and considering degenerate perturbation theory’s effects on them. Using this method, we give the first example of degenerate perturbation theory solving search on a graph whose evolution occurs in a subspace whose dimension grows with \(N\).

Keywords

Quantum search Quantum walks Quantum algorithms  Perturbation theory Grover’s algorithm 

Notes

Acknowledgments

Thanks to David Meyer for useful discussions. This work was partially supported by the European Union Seventh Framework Programme (FP7/2007-2013) under the QALGO (Grant Agreement No. 600700) project, and the ERC Advanced Grant MQC.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Faculty of ComputingUniversity of LatviaRigaLatvia

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