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Re-examining quantum walk advantages: A mean hitting time perspective.

Jan Wójcik1

  • 1University of Gdańsk, Institute of Theoretical Physics and Astrophysics, 80-308 Gdańsk, Poland.

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PubMed
Summary

Mean squared displacement may overstate quantum walk advantages. Mean hitting time (MHT) offers a clearer comparison, especially under stochastic resetting, revealing unique quantum walk dynamics.

Area of Science:

  • Quantum computing
  • Quantum walks
  • Complex systems

Background:

  • Mean squared displacement (MSD) is a common metric for comparing quantum and classical random walks.
  • Quantum walks exhibit non-Gaussian distributions, potentially limiting MSD's effectiveness.
  • Alternative metrics may better capture quantum walk nuances.

Purpose of the Study:

  • To propose and analyze mean hitting time (MHT) as a complementary metric for quantum-classical walk comparisons.
  • To investigate the impact of stochastic resetting on MHT for both quantum and classical walks.
  • To identify new signatures of quantum behavior in random walks.

Main Methods:

  • Analytical calculations of mean squared displacement and mean hitting time.
  • Comparison of quantum and classical walks under symmetric initial conditions.

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  • Analysis of stochastic resetting effects on quantum and classical walks.

    • Main Results:

    • Quantum and classical walks show identical MHT for symmetric initial conditions with two detectors.
    • Quantum walks exhibit reduced MHT under stochastic resetting via quasimomentum redistribution.
    • Classical walks show no MHT benefit from stochastic resetting.
    • Quantum advantage in MHT degrades with noise, leading to classical behavior.

    Conclusions:

    • Mean hitting time provides a valuable, complementary perspective to MSD for comparing quantum and classical walks.
    • Stochastic resetting reveals a distinct quantum advantage in MHT, offering a signature of quantum behavior.
    • MHT under stochastic resetting is a promising metric for characterizing quantum walks on noisy devices.