Mixing and Decoherence in Continuous-time quantum walks on long-range interacting cycles

Abstract

We study the effect of small decoherence in continuous-time quantum walks on long-range interacting cycles, which are constructed by connecting all the two nodes of distance m on the cycle graph. In our investigation, each node is continuously monitored by an individual point contact, which induces the decoherence process. We obtain the analytical probability distribution and the mixing time upper bound. Our results show that, for small rates of decoherence, themixing time upper bound is independent of distance parameter m and is proportional to inverse of decoherence rate.

15 pages, 2 Figures

References in corpus (12)

• Optimizing the discrete time quantum walk using a SU(2) coin
• Relaxation and Zeno effect in qubit measurements
• Coherent exciton transport in dendrimers and continuous-time quantum walks
• Quantum transport on small-world networks: A continuous-time quantum walk approach
• Continuous-time Quantum Walks on a Cycle Graph
• 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
• Quantum and classical diffusion in small-world networks
• Quantum central limit theorem for continuous-time quantum walks on odd graphs in quantum probability theory
• Coherent exciton transport and trapping on long-range interacting cycles

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