My totally unsubstantiated and made up take on this is that perhaps consciousness happens in the quantum side of things that we can't either measure or really simulate because we can never really observe it, e.g. we can simulate quantum behavior quite well, but only based on the observed behavior, the particle side of the particle wave duality, we don't really know for sure what happens before the wave function collapses, we just know it's a probability space (which we can predict for repeated experiments very accurately, but we don't really know how to predict a single particle, we don't even know how to measure all of its properties at the same time let alone predict it).
If consciousness happens in that no locality / no realism area of the unobserved quantum state, then perhaps this is why we can't simulate it with existing technology. I have no basis to this thought other than a hunch. It also somewhat helps explain determinism vs free will (although superdeterminism is also an explanation, one that I don't really like)
"... we don't even know how to measure all of its properties at the same time ..."
I assume you're referring to Heisenberg's Uncertainty Principle [1]. If you are, then this shows a fundamental misunderstanding of it. The uncertainty principle describes a fundamental property of quantum systems. It has nothing to do with our measurement technology.
The brain is too hot to rely on large-scale quantum entanglement. Any quantum effects that are relevant to the functioning of the brain are likely to be very small-scale and have some boring, easily-simulated effect like making ion pumps more efficient.
