Efficient error models for fault-tolerant architectures and the Pauli twirling approximation

The design and optimization of realistic architectures for fault-tolerant quantum computation requires error models that are both reliable and amenable to large-scale classical simulation. Perhaps the simplest and most practical general-purpose method for constructing such an error model is to twirl a given completely positive channel over the Pauli basis, a procedure we refer to as the Pauli twirling approximation (PTA). In this work we test the accuracy of the PTA for a small stabilizer measurement circuit relevant to fault-tolerant quantum computation, in the presence of both intrinsic gate errors and decoherence, and find excellent agreement over a wide range of physical error rates. The combined simplicity and accuracy of the PTA, along with its direct connection to the χ matrix of process tomography, suggests that it be used as a standard reference point for more refined error model constructions.