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Quantum Random Walk in Periodic Potential on a Line |
| LI Min, ZHANG Yong-Sheng**, GUO Gunag-Can |
Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026
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| Cite this article: |
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LI Min, ZHANG Yong-Sheng, GUO Gunag-Can 2013 Chin. Phys. Lett. 30 020304 |
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Abstract We investigate the discrete-time quantum random walks on a line in periodic potential. The probability distribution with periodic potential is more complex compared to the normal quantum walks, and the standard deviation σ has interesting behaviors for different period q and parameter θ. We study the behavior of standard deviation with variation in walk steps, period, and θ. The standard deviation increases approximately linearly with θ and decreases with 1/q for θ∈(0,π/4), and increases approximately linearly with 1/q for θ∈[π/4,π/2). For θ∈(π/4, 3π/4), the transmission is larger than the reflection, with sensibility the diffussion will be accelerated. However, when q=2, the standard deviations are nearly the same, and when q>2, the standard deviation will decrease.
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Received: 15 November 2012
Published: 02 March 2013
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| PACS: |
03.67.Lx
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(Quantum computation architectures and implementations)
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05.30.-d
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(Quantum statistical mechanics)
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05.40.Fb
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(Random walks and Levy flights)
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