Diagrammatic approach to quantum search

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 \(N\).

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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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Correspondence to Thomas G. Wong.

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Wong, T.G. Diagrammatic approach to quantum search. Quantum Inf Process 14, 1767–1775 (2015). https://doi.org/10.1007/s11128-015-0959-3

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Keywords

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