  We give a computational complexity argument against the feasibility of
quantum computers. We identify a very low complexity class of probability
distributions described by noisy intermediate-scale quantum computers, and
explain why it will allow neither good-quality quantum error-correction nor a
demonstration of "quantum supremacy." Some general principles governing the
behavior of noisy quantum systems are derived. Our work supports the "physical
Church thesis" studied by Pitowsky (1990) and follows his vision of using
abstract ideas about computation to study the performance of actual physical
computers.
