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A one-dimensional quantum walk with multiple-rotation on the coin.
Peng Xue1, Rong Zhang1, Hao Qin1
1Department of Physics, Southeast University, Nanjing 211189, China.
Scientific Reports
|January 30, 2016
Summary
We analyzed a one-dimensional quantum walk with two coin rotations. The study found that this quantum walk exhibits ballistic behavior and no localization, even with multiple rotations.
Area of Science:
- Quantum mechanics
- Quantum computation
Background:
- Quantum walks are a fundamental primitive in quantum computation.
- Understanding the behavior of quantum walks with modified parameters is crucial for developing new quantum algorithms.
Purpose of the Study:
- To introduce and analyze a one-dimensional quantum walk with two time-independent coin rotations.
- To investigate the influence of a second coin rotation on quantum walk properties.
- To determine if localization occurs in this modified quantum walk model.
Main Methods:
- Analysis of a one-dimensional quantum walk model.
- Inclusion of two time-independent rotations on the coin.
- Asymptotic solution in the long-time limit.
Main Results:
- The quantum walk exhibits ballistic behavior.
- The variance shows quadratic growth, indicating no localization.
- The combined coin rotation operator is unitary.
Conclusions:
- The analyzed quantum walk demonstrates ballistic transport without localization.
- The findings suggest that multiple time-independent rotations do not induce localization.
- This model provides insights into designing quantum walks for computational purposes.
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