Quantum Information, Mathematical Knowledge, and the Laws of Physics

Quantum computing research is deepening our understanding of physics and mathematics. This represents an intellectual payoff from quantum computing, whether or not scalable quantum computers are ever built. We already know that at least one of the following must be true: the Extended Church-Turing Thesis is wrong; textbook quantum mechanics is wrong; there’s a fast way to break public key encryption with classical computers. Each of these has immense implications, from philosophical to social.