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The present work is motivated by the need for robust, large-scale coherent states that can play possible roles as quantum resources. A challenge is that large, complex systems tend to be fragile. However, emergent phenomena in classical systems tend to become more robust with scale. Do these classical systems inspire ways to think about robust quantum networks? This question is studied by characterizing the complex quantum states produced by mapping interactions between a set of qubits from structure in graphs. We focus on maps based on k-regular random graphs where many edges were randomly deleted. We ask how many edge deletions can be tolerated. Surprisingly, it was found that the emergent coherent state characteristic of these graphs was robust to a substantial number of edge deletions. The analysis considers the possible role of the expander property of k-regular random graphs.

 

Some of the fundamentals of quantum information science are described, including the concepts of quantum resources, quantum states and mixedness of states. The explanations are detailed and include a combination of basic facts with fully worked examples, and some more advanced topics. The principles of quantum information are illustrated with chemical examples drawn from singlet fission, photophysics of radicals, molecular excitons, electron transfer and so on. Suggestions for prospects and challenges for the field are discussed.

 

Light absorption by molecular exciton states in disordered networks is studied. The main purpose of this paper is to look at how phases of the intermediate ground–excited state superposition interfere during the absorption process. How does this phase average enable, or suppress, absorption to a delocalized state? To address this question, a theory for phase oscillators is used to predict the purity of the collective excited state of the network. The results of the study suggest that collective absorption by molecular exciton states requires a sufficiently large electronic coupling between molecules in the network compared to the random distribution of transition energies at the sites, even when the molecular network is completely isolated from the environment degrees of freedom. The ‘dividing line’ between absorption to a mixture of, essentially, localized excited states and coherent excitation of a pure delocalized exciton state is suggested to be predicted by the threshold of phase synchronization.