Efficiently characterize stabilizer mixtures for noisy two-qubit Choi states

Determine efficiently whether a mixed Choi state of a general two-qubit gate subjected to local depolarizing noise belongs to the convex hull of stabilizer states, thereby enabling computation of the corresponding noise threshold and comparison with the fermionic convex-Gaussian bound.

Background

The paper notes that a direct comparison with the Clifford case would require analyzing a general two-qubit gate and finding the local depolarizing noise level at which its Choi state enters the convex hull of stabilizer states. Unlike fermionic convex Gaussianity, efficient membership testing for mixed stabilizer mixtures is not established in the paper. The authors mention robustness of magic as a possible linear-programming-based tool, while noting that optimizing over gate parameters may be difficult.