New research tries to explain consciousness with quantum physics

Lots of handwavyness, nothing related to the biochemical activity of actual neurons.

"...intricate network and that the consciousness this produces should obey the rules of quantum mechanics..."

This is not a statement of mechanism, for it to be such one would need to make some statement about the behavior of proteins or other molecules and how they interact within the rules of quantum mechanics. There has been a tiny bit of research on biophotons, but nothing in that research necessarily suggests some neuronal mechanism highly dependant on some uniquely quantum feature.

Many biological systems are suggested to depend on quantum mechanical effects. See quantum biology.

There is such a thing as plant intelligence. Could they have quantum intelligence then? Do dolphins and elephants have quantum consciousness?

I think we would understand brains better if we would stay with rat brains instead of chasing flimsy concepts like consciousness and soul. Rodents don't require either apparently, so this gives us an opportunity to focus on their neurobiology.

This new knowledge of quantum fractals could provide the foundations for scientists to experimentally test the theory of quantum consciousness. If quantum measurements are one day taken from the human brain, they could be compared against our results to definitely decide whether consciousness is a classical or a quantum phenomenon.

The idea that "consciousness" will somehow just magically spring forth from what we call a "computer" is the modern equivalent of alchemy. Pure fantasy without any scientific basis.