Abstract
Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting systems. In particular, the transport properties strongly depend on the initial state and specific features of the graph under investigation. In this paper, we address the role of graph topology, and investigate the transport properties of graphs with different regularity, symmetry, and connectivity. We neglect disorder and decoherence, and assume a single trap vertex that is accountable for the loss processes. In particular, for each graph, we analytically determine the subspace of states having maximum transport efficiency. Our results provide a set of benchmarks for environment-assisted quantum transport, and suggest that connectivity is a poor indicator for transport efficiency. Indeed, we observe some specific correlations between transport efficiency and connectivity for certain graphs, but, in general, they are uncorrelated.
Highlights
A continuous-time quantum walk (CTQW) is the quantum mechanical counterpart of the continuous-time random walk
We address the transport by CTQW on the above mentioned graphs, which are different in terms of regularity, symmetry, and connectivity, and we assess the transport efficiency for initial states that are localized at a vertex and for an initial superposition of two vertices
Just by focusing on the transport efficiency for an initial state localized at a vertex, we observe that the connectivity is a poor indicator for the transport efficiency
Summary
A continuous-time quantum walk (CTQW) is the quantum mechanical counterpart of the continuous-time random walk. The CTQW Hamiltonian modeling transport processes shows similarities with the CTQW Hamiltonian adopted to study the spatial search. Both of them consist of the sum, with proper coefficients, of the Laplacian matrix, which is accountable for the motion of the walker on the graph, and the projector onto one or more specific vertices. We address the transport by CTQW on the above mentioned graphs, which are different in terms of regularity, symmetry, and connectivity, and we assess the transport efficiency for initial states that are localized at a vertex and for an initial superposition of two vertices. In Appendix B, we determine the basis states spanning such a subspace for each graph considered
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
