The problem with this idea is that quantum mechanical systems tend to remain coherent for extremely short times when they are coupled to an environment. For instance, it might be plausible that a couple of atoms become superposed and remain uncorrelated with the rest of a cell for a few nanoseconds, but this superposition will rapidly decohere (on a time scale much smaller than that of cell division). You're certainly not going to be able to preserve a quantum-mechanical superposition long enough to influence the evolution of a species!
(Incidentally, rapid decoherence is also a major problem for those people who want to construct quantum computers. You may be able to store a few qubits in a couple of atoms in a single molecule long enough to perform a simple calculation, but to do anything nontrivial would require hundreds of qubits, and no one knows how to keep such a large system from decohering too quickly.)
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The problem with this idea is that quantum mechanical systems tend to remain coherent for extremely short times when they are coupled to an environment. For instance, it might be plausible that a couple of atoms become superposed and remain uncorrelated with the rest of a cell for a few nanoseconds, but this superposition will rapidly decohere (on a time scale much smaller than that of cell division). You're certainly not going to be able to preserve a quantum-mechanical superposition long enough to influence the evolution of a species!
(Incidentally, rapid decoherence is also a major problem for those people who want to construct quantum computers. You may be able to store a few qubits in a couple of atoms in a single molecule long enough to perform a simple calculation, but to do anything nontrivial would require hundreds of qubits, and no one knows how to keep such a large system from decohering too quickly.)