First things first.
For animals to evolve ergo they must encode more information or else they violate this central tennant of QM or don't evolve take your pick.
You seem to be equating evolution with an increase in complexity. That is not necessarily so. Using your computer comparison there are still a lot of applications out there that use 4 bit computers. They are such things as microwaves, locks, etc. In fact I suspect that there are a lot more 4 bit processors in use than all the other formats combined. Their uses are evolving, but they aren't getting more complex. Bacteria are the same way. They are continually evolving, but they aren't getting more complex. Evolution is basically variation in response to changes in the environment. That doesn't necessarily imply a need to become more complex, just different.
The variations are encoded in the DNA which is a string of molecules, well actually a molecule with a lot of identical nucleotides. The encoding is in the arrangement of the nucleotides. There is no need to study quantum spins to determine the code, just as there is no need to study the quantum spins of the atoms in a computer memory. All you need to know is the state of the memory element. You just need to know whether it is on or off. The information in the computer is in the series of on/off states, the information in the DNA is in the composition of each nucleotide of the string, ATD, CDG, etc. The quantum spin of the particles that make up the nucleotides doesn't enter into the coding.
All of the atoms in the DNA are held together in their strict alignments by QM, but after they get together it is just the sequence they are in that counts.