Efficient percolation simulations for lossy photonic fusion networks

Abstract

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 non-standard 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 perform the corresponding percolation simulation efficiently. We demonstrate our algorithms by using them to characterize exemplary fusion networks and graph states. The used source code is provided as an open-source repository.