Advertisement

Quantum Information Processing

, Volume 12, Issue 1, pp 459–466 | Cite as

Local controllability of quantum systems

  • Zbigniew PuchałaEmail author
Open Access
Article

Abstract

We give a criterion that is sufficient for controllability of multipartite quantum systems. We generalize the graph infection criterion to the quantum systems that cannot be described with the use of a graph theory. We introduce the notation of hypergraphs and reformulate the infection property in this setting. The introduced criterion has a topological nature and therefore it is not connected to any particular experimental realization of quantum information processing.

Keywords

Quantum control Local control Hypergraph 

Notes

Acknowledgments

We acknowledge the financial support by the Polish National Science Centre under the grant number N N514 513340.

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

References

  1. 1.
    Albertini, F., D’Alessandro, D.: Notions of controllability for quantum mechanical systems. In: Decision and control. Proceedings of the 40th IEEE conference on, vol. 2, pp. 1589–1594. IEEE (2001)Google Scholar
  2. 2.
    Albertini F., D’Alessandro D.: The Lie algebra structure and controllability of spin systems. Linear Algebra Appl. 350(1–3), 213–235 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Albertini F., D’Alessandro D.: Notions of controllability for bilinear multilevel quantum systems. Autom. Control, IEEE Trans. 48(8), 1399–1403 (2003)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Baxter R., Wu F.: Exact solution of an ising model with three-spin interactions on a triangular lattice. Phys. Rev. Lett. 31(21), 1294–1297 (1973)ADSCrossRefGoogle Scholar
  5. 5.
    Berge C.: Graphs and Hypergraphs, vol. 6. Elsevier, North Holland, NY (1976)Google Scholar
  6. 6.
    Burgarth D., Bose S., Bruder C., Giovannetti V.: Local controllability of quantum networks. Phys. Rev. A 79(6), 60–305 (2009)CrossRefGoogle Scholar
  7. 7.
    Burgarth D., Giovannetti V.: Full control by locally induced relaxation. Phys. Rev. Lett. 99(10), 100–501 (2007)CrossRefGoogle Scholar
  8. 8.
    D’Alessandro D.: Introduction to Quantum Control and Dynamics. Chapman & Hall, London (2008)zbMATHGoogle Scholar
  9. 9.
    Elliott D.: Bilinear Control Systems: Matrices in Action. Springer, Berlin (2009)zbMATHGoogle Scholar
  10. 10.
    Goldschmidt Y. et al.: Solvable model of the quantum spin glass in a transverse field. Phys. Rev. B Condens. Matter 41(7), 4858 (1990)MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    Heule R., Bruder C., Burgarth D., Stojanovió V.M.: Local quantum control of Heisenberg spin chains. Phys. Rev. A 82(5), 052–333 (2010). doi: 10.1103/PhysRevA.82.052333 CrossRefGoogle Scholar
  12. 12.
    Jurdjevic V., Sussmann H.: Control systems on lie groups. J. Diff. Equ. 12(2), 313–329 (1972)MathSciNetADSzbMATHCrossRefGoogle Scholar
  13. 13.
    Lou P.: Thermal and spin transports in spin-1/2 extended xy chain. Phys. Status Solidi (B) 241(6), 1343–1349 (2004)ADSCrossRefGoogle Scholar
  14. 14.
    Titvinidze I., Japaridze G.: Phase diagram of the spin extended model. Eur. Phys. J. B-Condens. Matter Complex Syst. 32(3), 383–393 (2003)CrossRefGoogle Scholar
  15. 15.
    Turinici G., Rabitz H.: Quantum wavefunction controllability. Chem. Phys. 267(1–3), 1–9 (2001)ADSCrossRefGoogle Scholar
  16. 16.
    Turinici G., Rabitz H.: Wavefunction controllability for finite-dimensional bilinear quantum systems. J. Phys. A Math. Gen. 36, 2565 (2003)MathSciNetADSzbMATHCrossRefGoogle Scholar

Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Institute of Theoretical and Applied InformaticsPolish Academy of SciencesGliwicePoland

Personalised recommendations