q-energy-hackathon-i / Evolutionary scale-free networks

The study of networks and transport in networks is of great interest for the sport-science field. For instance, the iterative process of building a team for the Olympics, which consists in evaluating the collective performance through the permutation of athletes inside the team, is a key process in maximizing the team’s performance and winning a medal. Another example includes the modeling of the communication between athletes in a team during a match, which changes with time, or the identification of the "institutional trajectories" of athletes, i.e., assessing the structures (alternatively, the coaches) which are critical in the institutional network of sport organizations. More generally, transport in complex (or scale-free) networks is relevant for various natural and artificial systems. These networks have a degree distribution that follows a power law $P(k) \sim k^{-\gamma}$ (or truncated power law), where $k$ is the node degree and $\gamma$ is an exponent. Natural and artificial systems forming such networks can be altered with time, and often exhibit properties related to the percolation phenomena, where links are lost or destroyed with time. This can illustrate the loss of information between athletes during a match (due to the adversary breaking a link between two athletes, for instance), or the loss of a path (i.e., possibility to move from one structure/coach to another) between two institutional structures (or coaches), which may endanger the sport organization at the national level. Previous studies have shown that scale-free networks are fragile and prone to collapse. This was demonstrated theoretically and for multiple dynamical real-world systems, such as (species) evolution and ecosystems, the financial sector, and social networks. The stability of such systems can be jeopardized with the removal of just one element, possibly leading to collapse.

In this hackathon, we aim at modeling a simplified version of these processes in quantum computers. The ultimate objective is to avoid the computing bottleneck of the whole process (construction of the graph + solving equation (2), and see section 2.3) that occurs when simulating large networks with millions of nodes.

Specific resources: [1, 2]