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Slow transport by continuous time quantum walks.

Oliver Mülken1, Alexander Blumen

  • 1Theoretische Polymerphysik, Universität Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg i.Br., Germany. oliver.muelken@physik.uni-freiburg.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
PubMed
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Continuous time quantum walks (CTQWs) do not always outperform classical random walks (CTRWs). On a specific graph, CTQWs show slower transport in one direction but faster transport when starting from a symmetric state.

Area of Science:

  • Quantum mechanics
  • Quantum computation
  • Complex systems

Background:

  • Continuous time quantum walks (CTQWs) are quantum analogs of classical random walks.
  • The comparative performance of CTQWs and continuous time random walks (CTRWs) is an active area of research.
  • Previous studies suggested potential advantages of CTQWs over CTRWs in graph traversal.

Purpose of the Study:

  • To investigate the performance of CTQWs compared to CTRWs on a specific graph structure.
  • To analyze the influence of initial conditions on the transport dynamics of CTQWs.
  • To determine the conditions under which CTQWs may exhibit slower or faster transport than CTRWs.

Main Methods:

  • Theoretical analysis of quantum walk dynamics on a specialized graph.

Related Experiment Videos

  • Comparison of propagation speeds and graph penetration between CTQWs and CTRWs.
  • Examination of transport properties under different initial quantum states, including localized and symmetric superpositions.

    • Main Results:

    • CTQWs do not universally outperform CTRWs; performance is direction-dependent.
    • On the considered graph, CTQWs exhibit slower transport in one propagation direction compared to CTRWs.
    • A totally symmetric initial superposition state significantly enhances CTQW transport speed.

    Conclusions:

    • The efficiency of CTQWs is not guaranteed and depends critically on the graph topology and initial state.
    • Symmetric initial conditions can unlock faster transport regimes for CTQWs, potentially surpassing CTRWs.
    • This research highlights the nuanced relationship between quantum dynamics and classical transport phenomena.