Key points are not available for this paper at this time.
Recently, Hastings 0.3 for the honeycomb code compared to a threshold of 0.50.7 for the surface code in a controlled-not circuit model. In a circuit model with native two-body measurements, the honeycomb code achieves a threshold of 1.5p2.0, where p is the collective error rate of the two-body measurement gate - including both measurement and correlated data depolarization error processes. With such gates at a physical error rate of 103, we project that the honeycomb code can reach the teraquop regime with only 600 physical qubits.
Gidney et al. (Mon,) studied this question.