There's a naively fashionable idea that DNA is basically the same as a Turing tape.
It isn't. It may be true that biological systems can be understood in terms of information theory, but the information is in the entire ecosystem - including the sum total of all individuals and species and their previous and current state.
E.g. on Earth, the entire planetary ecosystem eventually evolved a species with the ability to understand quantum theory - which happened to be a useful adaption, at least for a while.
But you're not going to find an explicit formalism for Schrodinger's Equation in human DNA no matter how hard you look for it.