Quantum walk and fast protein-folding time

The Levinthal paradox states that it would be impossible for a protein to reach its native conformation in a physically meaningful time by randomly searching over all possible conformations. So far, it has been widely assumed that this random conformational search does not occur in the folding process, for which various putative hypotheses have had to be employed in model studies. Here we show that the quantum approach, describing the folding process as a quantum walk on a definite graph, gives rise to a fast protein-folding time. In terms of the conventional lattice model describing protein conformation, we introduce a procedure to enumerate all possible structures and then determine the definite connection graphs. Evaluating the mean first-passage time, we find it is much shorter than that obtained via random searching, and the magnitude of the quantum approach is reasonably in agreement with the experimental result. Some further discussions of various characteristic average quantities are also made by comparing both cases of quantum walk and classical random walk.