  One of simplest and most widely used error model in working with quantum
circuits is the Pauli Twirling Approximation (PTA). Restricting ourselves to
analysis of free dynamics of qubits we show explicitly how application of PTA
is equivalent to ignoring most of the quantum back action of the system and
give a general argument as to why this approximation leads to low logical error
rates in fault tolerant stabilizer circuits as compared to other quantum
channels. We provide numerical evidence that PTA's performance in modeling
noise gets worse as number of qubits increase.
