The effect of large-decoherence on mixing-time in Continuous-time quantum walks on long-range interacting cycles
arXiv:0910.5795 · doi:10.1088/0953-4075/43/2/025503
Abstract
In this paper, we consider decoherence in continuous-time quantum walks on long-range interacting cycles (LRICs), which are the extensions of the cycle graphs. For this purpose, we use Gurvitz's model and assume that every node is monitored by the corresponding point contact induced the decoherence process. Then, we focus on large rates of decoherence and calculate the probability distribution analytically and obtain the lower and upper bounds of the mixing time. Our results prove that the mixing time is proportional to the rate of decoherence and the inverse of the distance parameter () squared. This shows that the mixing time decreases with increasing the range of interaction. Also, what we obtain for is in agreement with Fedichkin, Solenov and Tamon's results \cite{FST} for cycle, and see that the mixing time of CTQWs on cycle improves with adding interacting edges.
16 Pages, 2 Figures
References in corpus (16)
- Spatial search by quantum walk
- Experimental Implementation of Discrete Time Quantum Random Walk on an NMR Quantum Information Processor
- Survival Probabilities in Coherent Exciton Transfer with Trapping
- Relaxation and Zeno effect in qubit measurements
- Quantum walks on quotient graphs
- Exact analytical results for quantum walks on star graph
- Investigation of continuous-time quantum walk by using Krylov subspace-Lanczos algorithm
- Continuous-time quantum walks on star graphs
- Investigation of Continuous-Time Quantum Walk Via Modules of Bose-Mesner and Terwilliger Algebras
- Continuous time quantum walks in phase space
- Coherent exciton transport and trapping on long-range interacting cycles
- Quantum central limit theorem for continuous-time quantum walks on odd graphs in quantum probability theory
- Universal Behavior of Quantum Walks with Long-Range Steps
- Reexamination of decoherence in quantum walks on the hypercube
- Slow Excitation Trapping in Quantum Transport with Long-Range Interactions
- Mixing and Decoherence in Continuous-time quantum walks on long-range interacting cycles