Quantum intelligence on protein folding pathways

We study the protein folding problem on the base of our quantum approach by considering the model of protein chain with nine amino-acid residues. We introduce the concept of distance space and its projections on a XY-plane, and two characteristic quantities, one is called compactness of protein structure and another is called probability ratio involving shortest path. The concept of shortest path enables us to reduce the 388×388 density matrix to a 2×2 one from which the von Neumann entropy reflecting certain quantum coherence feature is naturally defined. We observe the time evolution of average distance and compactness solved from the classical random walk and quantum walk, we also compare the features of the time-dependence of Shannon entropy and von Neumann entropy. All the results not only reveal the fast quantum folding time but also unveil the existence of quantum intelligence hidden behind in choosing protein folding pathways.