Figure 1 : Qubits and corresponding baths represented as white and black circles respectively.

From: Optimally combining dynamical decoupling and quantum error correction

Figure 1

Bath operators corresponding to different operators inside a box do not necessarily commute, while they do if the baths are in different boxes. The Hamiltonians considered are general within each box, but not between them. In (a) a diagram of the “local bath assumption” used in Ref. 27 is shown, while (b) represents the general scenario considered in fault-tolerance12,13,14. In (c) we illustrate one of our key results: domains are allowed to grow logarithmically in the size of the problem the FTQC is solving. The dark grey boxes represent such domains, each containing O[log(ktot)] physical qubits at the highest level of concatenation, where ktot is the total number of logical qubits. When two domains need to interact (light grey box), then the joint DD generator set is used and the locality of the bath is updated accordingly.