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Quantum walks with tuneable self-avoidance in one dimension.

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This study introduces quantum self-avoiding walks, a quantum computation method where walkers avoid revisiting locations. By tuning memory parameters, these walks can mimic quantum or classical random walks, offering new algorithmic possibilities.

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Area of Science:

  • Quantum computing
  • Quantum information science
  • Complex systems

Background:

  • Classical self-avoiding random walks (SAWs) are essential in modeling complex systems like protein folding.
  • Quantum walks (QWs) offer unique computational advantages over classical random walks.
  • Exploring quantum analogues of classical concepts like SAWs is crucial for advancing quantum algorithms.

Purpose of the Study:

  • To introduce and characterize a one-dimensional quantum self-avoiding walk (QSAW) with tunable self-avoidance.
  • To investigate the effects of memory recording and back-action on QSAW dynamics.
  • To explore the relationship between QSAWs and classical SAWs.

Main Methods:

  • Implementing a quantum walk with an auxiliary memory register to track visited sites.
  • Introducing tunable parameters for memory recording strength and memory back-action.
  • Analyzing the variance of the walker's distribution over time to quantify walk dynamics.

Main Results:

  • Demonstrated that QSAWs can reproduce ideal quantum or classical random walk statistics.
  • Showcased the ability to achieve diverse diffusive phenomena by adjusting self-avoidance parameters.
  • Observed a correspondence between QSAWs and classical SAWs in specific parameter regimes.

Conclusions:

  • QSAWs provide a versatile framework for quantum walks with controllable self-avoidance.
  • The QSAW model offers a pathway to bridge quantum and classical walk behaviors.
  • This research opens avenues for novel quantum algorithms inspired by self-avoiding walk principles.