Skip to main content
SpringerLink
Log in

Diagrammatic approach to quantum search

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

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 \(N\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Sakurai, J.J.: Modern Quantum Mechanics (Revised Edition). Addison Wesley, Boston (1993)

  2. Janmark, J., Meyer, D.A., Wong, T.G.: Global symmetry is unnecessary for fast quantum search. Phys. Rev. Lett. 112, 210502 (2014)

    ADS  Google Scholar 

  3. Meyer, D.A., Wong, T.G.: Connectivity is a poor indicator of fast quantum search. arXiv:1409.5876 [quant-ph] (2014)

  4. Childs, A.M., Goldstone, J.: Spatial search by quantum walk. Phys. Rev. A 70, 022314 (2004)

    ADS  MathSciNet  Google Scholar 

  5. Farhi, E., Goldstone, J., Gutmann, S., Sipser, M.: Quantum computation by adiabatic evolution. arXiv:quant-ph/0001106 (2000)

  6. Childs, A.M., Deotto, E., Farhi, E., Goldstone, J., Gutmann, S., Landahl, A.J.: Quantum search by measurement. Phys. Rev. A 66, 032314 (2002)

    ADS  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Faculty of Computing, University of Latvia, Raiņa bulv. 19, Riga, 1586, Latvia

    Thomas G. Wong

Authors
  1. Thomas G. Wong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas G. Wong.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-015-0959-3

Keywords

Search

Navigation