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Single-point position and transition defects in continuous time quantum walks.

Li ZJ, Wang JB - Sci Rep (2015)

Bottom Line: The number of bound states is found to be critically dependent on the defect parameters, and the localized probability peaks can be readily obtained by projecting the state vector of CTQW on to these bound states.The interference between two bound states are also observed in the case of a transition defect.The spreading of CTQW probability over the line can be finely tuned by varying the position and transition defect parameters, offering the possibility of precision quantum control of the system.

View Article: PubMed Central - PubMed

Affiliation: Institute of Theoretical Physics, Shanxi University, Taiyuan, 030006, China.

ABSTRACT
We present a detailed analysis of continuous time quantum walks (CTQW) with both position and transition defects defined at a single point in the line. Analytical solutions of both traveling waves and bound states are obtained, which provide valuable insight into the dynamics of CTQW. The number of bound states is found to be critically dependent on the defect parameters, and the localized probability peaks can be readily obtained by projecting the state vector of CTQW on to these bound states. The interference between two bound states are also observed in the case of a transition defect. The spreading of CTQW probability over the line can be finely tuned by varying the position and transition defect parameters, offering the possibility of precision quantum control of the system.

No MeSH data available.


The variation of bound energy with the strength of position defect.
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f1: The variation of bound energy with the strength of position defect.

Mentions: Choosing the parameter values ε = 2, γ = 1 and β = 0, we firstly examine the effects of a position defect on the quantum walk. In this case, there is always one bound state as long as α ≠ 0. The bound eigen energy λb as a function of α is shown in Fig. 1, in which λb = λ+ > ε + 2γ if α > 0 or λb = λ− < ε − 2γ if α < 0.


Single-point position and transition defects in continuous time quantum walks.

Li ZJ, Wang JB - Sci Rep (2015)

The variation of bound energy with the strength of position defect.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4555049&req=5

f1: The variation of bound energy with the strength of position defect.
Mentions: Choosing the parameter values ε = 2, γ = 1 and β = 0, we firstly examine the effects of a position defect on the quantum walk. In this case, there is always one bound state as long as α ≠ 0. The bound eigen energy λb as a function of α is shown in Fig. 1, in which λb = λ+ > ε + 2γ if α > 0 or λb = λ− < ε − 2γ if α < 0.

Bottom Line: The number of bound states is found to be critically dependent on the defect parameters, and the localized probability peaks can be readily obtained by projecting the state vector of CTQW on to these bound states.The interference between two bound states are also observed in the case of a transition defect.The spreading of CTQW probability over the line can be finely tuned by varying the position and transition defect parameters, offering the possibility of precision quantum control of the system.

View Article: PubMed Central - PubMed

Affiliation: Institute of Theoretical Physics, Shanxi University, Taiyuan, 030006, China.

ABSTRACT
We present a detailed analysis of continuous time quantum walks (CTQW) with both position and transition defects defined at a single point in the line. Analytical solutions of both traveling waves and bound states are obtained, which provide valuable insight into the dynamics of CTQW. The number of bound states is found to be critically dependent on the defect parameters, and the localized probability peaks can be readily obtained by projecting the state vector of CTQW on to these bound states. The interference between two bound states are also observed in the case of a transition defect. The spreading of CTQW probability over the line can be finely tuned by varying the position and transition defect parameters, offering the possibility of precision quantum control of the system.

No MeSH data available.