  We study the sensitivity to noise of |permanent(X)|^2 for random real and
complex n x n Gaussian matrices X, and show that asymptotically the correlation
between the noisy and noiseless outcomes tends to zero when the noise level is
{\omega}(1)/n. This suggests that, under certain reasonable noise models, the
probability distributions produced by noisy BosonSampling are very sensitive to
noise. We also show that when the amount of noise is constant the noisy value
of |permanent(X)|^2 can be approximated efficiently on a classical computer.
These results seem to weaken the possibility of demonstrating quantum-speedup
via BosonSampling without quantum fault-tolerance.
