If quantum computing was not possible, that would mean that everything we thought we knew about physics was hopelessly wrong. Physics would have to be much stranger - we'd have to give up on either locality (i.e. causation being limited by the speed of light), reversibility (closely related to conservation of energy), or nondeterminism in order to make the math work out. There are several papers in the literature that derive quantum mechanics from these or related assumptions (often together with some extra technical detail, that differs between approaches):
https://arxiv.org/abs/quant-ph/0101012 https://arxiv.org/abs/1011.6451 https://arxiv.org/abs/0911.0695