Are thoughts some kind of stochastic process

My argument is at atomic level, Heisenberg principle comes into picture and somehow stochastic nature is inbuilt into it.

Your argument applies more to CPUs than brains.

Like with neurons, transistors in a modern CPU signal each other with pulses of charged particles. In both cases, the motion of those messenger particles is stochastic; it is primarily determined by diffusion due to concentration gradients (with transistors, the E-field as as important, but not more). Thermal electrons move a lot faster than small organic molecules, though, so there is correspondingly more quantum uncertainty about their position.

So assuming neurons are what we think with, human thoughts are at least as deterministic as computer calculations.

I don't think we know enough about quantum mechanics. My understanding is that right now we model it as random behavior, but we have no real reason to believe its random rather than subject to some other factors that we can't/don't yet measure. (Someone correct me if I'm wrong).

That's what the Blue Brain project is currently doing. They are very convinced it's possible, but they are working on a molecular, not atomic level.