There are arguments, notably in "The Emperors New Mind", that assert that consciousness must be based on quantum mechanics in some ill-defined way and therefore that "algorithmic" computers can't therefore be conscious.
https://en.wikipedia.org/wiki/The_Emperor's_New_Mind
NB I didn't find this argument particularly strong, but it's a long time since I read it. The brain would have to be doing something spectacularly strange for it to be impossible for us to emulate in one way or another.