The key difference is that if the process is truly random the gene walks will not always be the shortest possible path you would expect some gene walks to be rather long and convoluted and some even dead ends because they are classical walks.
As I said we see this behavior with all things that can be described by QM that you only find the shortest path which we call a quantum walk.
The background of why it happens is straight forward
(
https://en.wikipedia.org/wiki/Quantum_walk)
=>Quantum walks exhibit very different features from classical random walks. In particular, they do not converge to limiting distributions and due to the power of quantum interference they may spread significantly faster or slower than their classical equivalents.
Again we have no idea why the behavior exists we are simply describing a quantum behavior.
If evolution has some sort of underpin that is working off the same thing(s) that QM describes they will quantum walk rather than classical random walk.
So I am being careful here to say I am not suggesting QM causes evolution but the other way around I am asking can evolution be described by QM.
Remember we are asking the same question of gravity is it classical or quantum?
What I am saying is biology is actually getting very close to a position they could test it which funny enough is actually closer than we are with gravity.
We can't add anything to what evolution is or why it is occurring but it might be nice to have a definitive answer on if it is a quantum process or a classical process ... biology as a science at the moment is assuming classical but I would like to see that tested.
The profile of a linear random quantum walk is not hard
Probability distribution resulting from one dimensional discrete time random walks. The quantum walk created using the Hadamard coin is plotted (blue) vs a classical walk (red) after 50 time steps
So the question is does a gene evolution follow that quantum probability distribution or not .... so which do we get with Gene evolution RED or BLUE ... answer that and you answer my question.