Efficient percolation simulations for lossy photonic fusion networks

TL;DR

This paper develops efficient algorithms for simulating non-standard percolation models relevant to photon loss tolerance in quantum photonic networks, enhancing understanding of their robustness.

Contribution

It introduces modified Newman-Ziff algorithms tailored for measurement-based photonic quantum computing models, enabling faster percolation threshold analysis.

Findings

Algorithms successfully characterize fusion networks and graph states.

Open-source code provided for community use.

Improved simulation efficiency for complex quantum network models.

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.