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

TL;DR

This paper evaluates the Pauli twirling approximation (PTA) as a simple, reliable, and accurate error model for fault-tolerant quantum computing architectures, demonstrating its effectiveness in simulating realistic quantum errors.

Contribution

The work tests and validates the accuracy of the PTA for stabilizer measurement circuits under realistic error conditions, proposing it as a standard reference for error modeling.

Findings

PTA shows excellent agreement with actual error models across various error rates.

PTA's simplicity and accuracy make it suitable for large-scale classical simulation.

PTA's connection to process tomography facilitates refined error model development.

Abstract

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 chi matrix of process tomography, suggests that it be used as a standard reference point for more refined error model constructions.