Categories, Quantum Computing, and Swarm Robotics: A Case Study

The swarms of robots are examples of artificial collective intelligence, with simple individual autonomous behavior and emerging swarm effect to accomplish even complex tasks. Modeling approaches for robotic swarm development is one of the main challenges in this field of research. Here, we present a robot-instantiated theoretical framework and a quantitative worked-out example. Aiming to build up a general model, we first sketch a diagrammatic classification of swarms relating ideal swarms to existing implementations, inspired by category theory. Then, we propose a matrix representation to relate local and global behaviors in a swarm, with diagonal sub-matrices describing individual features and off-diagonal sub-matrices as pairwise interaction terms. Thus, we attempt to shape the structure of such an interaction term, using language and tools of quantum computing for a quantitative simulation of a toy model. We choose quantum computing because of its computational efficiency. This case study can shed light on potentialities of quantum computing in the realm of swarm robotics, leaving room for progressive enrichment and refinement.