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Restart Expedites Quantum Walk Hitting Times.
1Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel.
Physical Review Letters
|February 17, 2023
Summary
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.
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.
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