Quantum logic automata generate class IV-like patterns and 1/f noise

Owing to recent advancements in brain science and AI, researchers tend to focus on the concept of self-organized criticality or the edge of chaos. On the other hand, quantum cognition, which is rooted in quantum mechanics, is promising for resolving various cognitive illusions. However, until recently, no connection between criticality and quantum mechanics was proposed. Gunji et al. (2024) recently introduced a linkage termed quantum logic automata, which encompasses not only quantum logic but also criticality characterized by power-law distributions. While quantum logic automata can be derived from various structures, only one of them has been proposed and discussed. Here, we define another type of quantum logic automata involving quantum logic and demonstrate that symmetric quantum logic automata lead to complex Class IV-like patterns and power-law distributions. Our findings support the association between criticality and quantum theory.