one line of evidence is that a purely classical analysis of the energy required to hold DNA together does not add up. It is possible that DNA is indeed quantum-efficient.

if Grover-algorithmic processing is some sort of fundamental property of nature, then you might expect the genetic material to be synthesized most efficiently when the machinery has a choice of 4 different nucleotides. And when translating these into proteins, a triplet code (which requires 3 processing steps) would function most efficiently when working with a palette of 20 amino acids. I will admit to being unusually susceptible to ideas like this, but that makes the hair stand up on the back of my neck.