Suppose the activation potential of a neuron is a quantum mechanical quantity that is probability driven
Or let's not suppose. Is it or isn't it? Even then, ultimately everything is probability driven, but that doesn't stop us doing very accurate simulations of physical phenomena. Balls interacting on a pool table touch and collide because they have molecules and atoms, but you don't need to calculate the position of every one of those to achieve realistic simulations.
Your computer can't model that to arbitrary precision, the probability density function is continuous, analog, not discrete.
Then model it with an analogue component - if you really do need such accuracy. It only really needs to be good enough that end result (consciousness in this case) is achievable.
Yes, a quantum model of your brain might choose vanilla where the real one would have chosen chocolate. Doesn't mean it's any less conscious.
All rather moot in any case, since the technological singularity only specifies that an intelligence beyond man's will come into being. Doesn't have to be human. Doesn't even have to be conscious in any sense that we'd recognise it.