Abstract
Transport across quantum networks underlies many problems, from state transfer on a spin network to energy transport in photosynthetic complexes. However, networks can contain dark subspaces that block the transportation, and various methods used to enhance transfer on quantum networks can be viewed as equivalently avoiding, modifying, or destroying the dark subspace. Here, we exploit graph theoretical tools to identify the dark subspaces and show that asymptotically almost surely they do not exist for large networks, while for small ones they can be suppressed by properly perturbing the coupling rates between the network nodes. More specifically, we apply these results to describe the recently experimentally observed and robust transport behaviour of the electronic excitation travelling on a genetically-engineered light-harvesting cylinder (M13 virus) structure. We believe that these mainly topological tools may allow us to better infer which network structures and dynamics are more favourable to enhance transfer of energy and information towards novel quantum technologies.
Highlights
Understanding the mechanisms of optimal transport of various quantities, such as energy or information, across some underlying topology is fundamental to many problems in physics and beyond
Different tools can be employed to deal with the dark subspaces: we can avoid them using smart initialisation, or suppress and destroy them by breaking the network symmetries through the use of control fields, noise, or disorder
Dark subspaces have a deep connection with topological symmetries, and can grow in size on more symmetric networks
Summary
Understanding the mechanisms of optimal transport of various quantities, such as energy or information, across some underlying topology is fundamental to many problems in physics and beyond (see, for instance [1,2,3], and references therein). There are numerous factors that need to be considered in order to achieve optimal transport: the dynamics of the network and the approximations used, the initial preparation and its coherence, the location of the target node, site energies, static disorder, noise, dissipation, etc. In this context, optimality refers to several transport features as absence of losses, short required time, and robustness (regardless of sudden changes of working conditions).
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