From [0] "If engineers ever succeed in making such quantum computers, it seems to me that the CAT is falsified; no classical theory can explain quantum mechanics." By "such quantum computers" he means computers that can run Shor's algorithm. "...but factoring a number with millions of digits into its prime factors will not be possible – unless fundamentally improved classical algorithms turn out to exist." by Gerard 't Hooft - Nobel Prize in Physics

[0] - https://arxiv.org/abs/1405.1548

EDIT: See page 79 of the referenced paper for the detailed argument.

I've heard a documentary about some physicists saying that quantum hasn't provided anything substantial yet and is hard to prove and often explainable without quantum theory. That said here is a starting point: https://en.wikipedia.org/wiki/Quantum_supremacy#Skepticism

Oded Goldreich, Stephen Wolfram, Leonid A. Levin and Gil Kalai are skeptics I know about.