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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 the transition defect.
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f4: The variation of bound energy with the strength of the transition defect.

Mentions: In this section, we focus on the effect of a single-point transition defect on the spreading properties of CTQW. We choose the parameters ε = 2,γ = 1 and α = 0, the bound energy as a function of transition defect strength is shown in Fig. 4. When /γ + β/ ≤ 1 (i.e. −2 ≤ β ≤ 0), no bound eigenstate exists, or else there are two bound states.


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 the transition defect.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f4: The variation of bound energy with the strength of the transition defect.
Mentions: In this section, we focus on the effect of a single-point transition defect on the spreading properties of CTQW. We choose the parameters ε = 2,γ = 1 and α = 0, the bound energy as a function of transition defect strength is shown in Fig. 4. When /γ + β/ ≤ 1 (i.e. −2 ≤ β ≤ 0), no bound eigenstate exists, or else there are two bound states.

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.