I mean, that is why they mention super-Turning processes like quantum based computing.

Quantum computing actually isn't super-Turing, it "just" computes some things faster. (Strictly speaking it's somewhere between a standard Turing machine and a nondeterministic Turing machine in speed, and the first can emulate the second.)

If we're nitpicking: quantum computing algorithms could (if implemented) compute certain things faster than the best classical algorithms we know. We don't know any quantum algorithms that are provably faster than all possible classical algorithms.

Well yeah, we haven't even proved that P != NP yet.

Either the brain violates the physical Church-Turing thesis or it's not.

If it does, well, it will take more time to incorporate those physical mechanisms into computers to get them on par with the brain.

I leave the possibility that it's "magic"[1] aside. It's just impossible to predict, because it will violate everything we know about our physical world.

[1] One example of "magic": we live in a simulation and the brain is not fully simulated by the physics engine, but creators of the simulation for some reason gave it access to computational resources that are impossible to harness using the standard physics of the simulated world. Another example: interactionistic soul.