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We propose a model of network growth in which the network is co-evolvingtogether with the dynamics of a quantum mechanical system, namely a quantumwalk taking place over the network. The model naturally generalizes theBarab\'{a}si-Albert model of preferential attachment and has a rich set oftunable parameters, such as the initial conditions of the dynamics or theinteraction of the system with its environment. We show that the model producesnetworks with two-modal power-law degree distributions, super-hubs, finiteclustering coefficient, small-world behaviour and non-trivial degree-degreecorrelations.

Co-evolution of networks and quantum dynamics: a generalization of preferential attachment