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.

中文翻译：

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图上连续时间量子行走的传输效率

连续时间量子行走描述了量子粒子（或激发）在图上随时间连续演化的传播。因此，它为模拟运输过程提供了一个自然框架，例如在光收集系统中。特别是，传输特性强烈依赖于所研究图的初始状态和特定特征。在本文中，我们解决了图拓扑的作用，并研究了具有不同规律性、对称性和连通性的图的传输特性。我们忽略了无序和退相干，并假设有一个对损失过程负责的陷阱顶点。特别是，对于每个图，我们分析确定具有最大传输效率的状态的子空间。我们的结果为环境辅助量子传输提供了一组基准，并建议连通性是运输效率的一个糟糕指标。事实上，我们观察到某些图的传输效率和连通性之间存在一些特定的相关性，但总的来说，它们是不相关的。