Percolação na Internet Quântica

Abstract

The area of Network Science has drawn huge attention from the scientific community due to its importance and interdisciplinary, promoting the integration of several other fields of knowledge. This is mainly because this area allows us to simulate real systems and formulate theoretical models about a wide range of phenomena. The Quantum Internet is included in a series of potential new applications called Quantum Technologies 2.0. This type of technology, in theory, will revolutionize the way we communicate. In principle, the Quantum Internet is grounded on the conjecture of distributing entanglement between the sites that constitute it to perform tasks that are impossible using the current Internet. This work provides a statistical analysis of the Quantum Internet network through the Percolation Theory. Percolation theory allows a simple and sophisticated description of a transition phase based on an order parameter. This dissertation begins with a general presentation of Network Theory and Percolation Theory concepts and foundations, where our study is ruled. Then, we reproduce the Quantum Internet model through optical fibers (OFBQI) for 𝜌 = 0.0002, where 𝜌 is the density of sites in the network. Combining the concepts studied and the OFBQI model, we investigated the point at which a transition phase from the percolating network to a disconnected network occurs. We use as an order parameter the relative size of the largest percolating cluster, 𝑚 = 𝑁𝐺/𝑁, 𝑁𝐺 is the size of the largest connected component (a subgraph) and 𝑁 is the size of the network. We show, through the Binder cumulative, that the fraction of sites removed that completely disconnects the network occurs in 𝑓𝑐 = 0.659, which turns out to be independent of the size of the system. Finally, we find the critical percolation exponents 𝛽, 𝛾, 𝜈, 𝜎, 𝜏 and the fractal dimension of the percolating cluster 𝑑𝑓 for the Quantum Internet.