Fig. 5: Using flag qubit gadgets to detect errors on qubit 1.
From: Efficient fault-tolerant implementations of non-Clifford gates with reconfigurable atom arrays
Here only the relevant gates in the distillation circuit are shown. The flag qubit gadgets are colored blue. If an X error occurs on qubit 1 within the flag qubit gadgets, their corresponding flag qubit will be measured − 1 and this round of distillation should be discarded. However, a Z error on the control qubit (1) of the leftmost blue CNOT gate can be propagated to qubits 1, 5, 7, 8, 11, which is a logical Z operator. As a result, this flag gadget can reduce the linear dependence of the output error from 3.5p to 2.5p.
