Quantum network is a set of nodes connected with channels, through which the nodes communicate photons and classical information. Classical structural complexity of a quantum network may be defined through its physical structure, i.e. mutual position of nodes and channels connecting them. We show here that the classical structural complexity of a quantum network does not restrict the structural complexity of entanglement graphs, which may be created in the quantum network with local operations and classical communication. We show, in particular, that 1D quantum network can simulate both simple entanglement graphs such as lattices and random graphs and complex small-world graphs.
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