A dynamical interpretation of the Pauli Twirling Approximation and Quantum Error Correction

Abstract: 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.