Efficient percolation simulations for lossy photonic fusion networks

The study of percolation phenomena has various applications ranging from social networks or materials science to quantum information. The most common percolation models are bond or site percolation for which the Newman-Ziff algorithm enables an efficient simulation. Here, we consider several nonstandard percolation models that appear in the context of measurement-based photonic quantum computing with so-called graph states and fusion networks. The associated percolation thresholds determine the tolerance to photon loss in such systems and we develop modifications of the Newman-Ziff algorithm to efficiently perform the corresponding percolation simulations. We demonstrate our algorithms by using them to characterize exemplary fusion networks and graph states.