  Results are presented of a large-scale simulation of the quantum adiabatic
search (QuAdS) algorithm in the presence of noise. The algorithm is applied to
the NP-Complete problem Exact Cover 3 (EC3). The noise is assumed to
Zeeman-couple to the qubits and its effects on the algorithm's performance is
studied for various levels of noise power, and for 4 different types of noise
polarization. We examine the scaling relation between the number of bits N (EC3
problem size) and the algorithm's noise-averaged median run-time <T(N)>. Clear
evidence is found of the algorithm's sensitivity to noise. Two fits to the
simulation results were done: (1) power-law scaling <T(N)> = aN**b; and (2)
exponential scaling <T(N)> = a[exp(bN) - 1]. Both types of scaling relations
provided excellent fits. We demonstrate how noise leads to decoherence in
QuAdS, estimate the amount of decoherence in our simulations, and derive an
upper bound for the noise-averaged QuAdS success probability in the weak noise
limit appropriate for our simulations.
