  We study the performance of distance-three surface code layouts under
realistic multi-parameter noise models. We first calculate their thresholds
under depolarizing noise. We then compare a Pauli-twirl approximation of
amplitude and phase damping to amplitude and phase damping. We find the
approximate channel results in a pessimistic estimate of the logical error
rate, indicating the realistic threshold may be higher than previously
estimated. From Monte-Carlo simulations, we identify experimental parameters
for which these layouts admit reliable computation. Due to its low resource
cost and superior performance, we conclude that the 17-qubit layout should be
targeted in early experimental implementations of the surface code. We find
that architectures with gate times in the 5-40 ns range and T1 times of at
least 1-2 us range will exhibit improved logical error rates with a 17-qubit
surface code encoding.
