Random Networks with Quantum Boolean Functions

We propose quantum Boolean networks, which can be classified as deterministic reversible asynchronous Boolean networks. This model is based on the concept of quantum Boolean functions. A quantum Boolean network is a Boolean network where the functions associated with the nodes are quantum Boolean functions. We study some properties of this novel model and, using a quantum simulator, we study how the dynamics change in function of the connectivity of the network and the set of operators we allow. For some configurations, the behavior of this model resembles that of reversible Boolean networks (RevBN), while for other configurations a more complex dynamics can emerge. For example, cycles larger than 2^N were observed. Additionally, using a scheme akin to one used previously with random Boolean networks, we computed the average entropy and complexity of the networks. As opposed to classic random Boolean networks, where “complex” dynamics are restricted mainly to a connectivity close to a phase transition, quantum Boolean networks can exhibit stable, complex, and unstable dynamics independently of their connectivity.