Fig. 1

Embedding rotated surface code. (a) and (b) Qubit arrangements of the rotated surface code in the square and heavy-hexagon lattices. The logical Z and X operators are represented by the purple and orange solid lines, respectively. (c) and (d) The stabilizers of the code are divided into two sub-groups. (e) A sub-round syndrome extraction circuit measures weight-four stabilizers including those at the side boundaries within the same sub-group. The first and last two layers of CNOT gates can be executed in parallel along with the former and latter sub-rounds. (f) Subroutine circuits for measuring weights-two and -one Z stabilizers at top and bottom boundaries.