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Restart Expedites Quantum Walk Hitting Times.

R Yin1, E Barkai1

  • 1Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel.

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|February 17, 2023
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Summary
This summary is machine-generated.

We introduce quantum hitting times with restart for quantum walks. Restarting quantum walks overcomes dark states and Zeno-blocking, revealing novel quantum oscillation effects on detection times.

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Area of Science:

  • Quantum mechanics
  • Quantum information theory
  • Quantum computing

Background:

  • Classical first-passage times with restart are widely used.
  • The quantum analogue of hitting times with restart is not well-understood.
  • Dark states and Zeno effects pose challenges in quantum detection.

Purpose of the Study:

  • To investigate quantum hitting times with restart.
  • To analyze the impact of quantum oscillations on restart strategies.
  • To overcome limitations of dark states and Zeno effects in quantum walks.

Main Methods:

  • Utilizing a monitored quantum walk.
  • Implementing a restart strategy for the quantum walker.
  • Analyzing the mean detection time and optimal restart policies.

Main Results:

  • Restarting eliminates dark states while preserving ballistic propagation.
  • Quantum oscillations introduce instability in mean detection times.
  • Optimal restart times exhibit staircase-like behavior with sudden drops.
  • Restart overcomes Zeno-blocking, making detection possible.
  • Optimal restart time becomes insensitive to sampling period in the Zeno limit.

Conclusions:

  • Restarting is a viable strategy for quantum detection problems.
  • Quantum oscillations significantly influence restart dynamics.
  • The proposed method offers a way to manage quantum walk detection effectively.