Comments on "Fault-Tolerant Quantum Computation for Local Non-Markovian Noise"

In the recent paper Terhal and Burkard derived a threshold result for fault-tolerant quantum computation under the assumption of the non-Markovian noise and claimed to rebut the objections rised by Alicki and Horodecki's. The purpose of this note is to show that the main condition used by Terhal and Burkard, although looking quite innocently, implies the assumption of the extremally low probability error per single quantum gate - p < 10^{-8} - 10^{-12} - i.e. the square of the expected threshold value for the case of Markovian noise.