Comment by oh_my_goodness

Gah, I wrote the wrong thing. If each probability is 50% +- 10^{-6} then the amplitudes are matched to within around 2 times 10^{-6}.

But when N>2 this gets tougher rapidly.

If we add 10^12 complex amplitudes and each one is off by one part in 10^{-6}, we could easily have serious problems with the accuracy of the sum. And 10^12 amplitudes is "only" around 40 qubits.