Extended Data Fig. 1: Surface code and transversal operations.
From: Low-overhead transversal fault tolerance for universal quantum computation
(a) Illustration of the surface code. White circles indicate data qubits. Orange (green) plaquettes are Z (X) stabilizers. The logical \(\overline{Z}\) (\(\overline{X}\)) operator runs vertically (horizontally), and we choose our convention for fixing Z (X) stabilizers to be performing a chain of X (Z) flips to the left (bottom) boundary, as illustrated by the red line. (b) Illustration of transversal \(\overline{H}\) gate, consisting of transversal H gates followed by a reflection along the diagonal. Note that this differs from the usual transversal \(\overline{H}\) gate, which applies a rotation in the second step. For the non-rotated surface code, both choices map X (Z) stabilizers to Z (X) stabilizers and hence are valid, but our choice leads to a smaller transversal partition size for the full circuit. (c) Illustration of transversal \(\overline{S}\) gate, consisting of S and S† gates along the diagonal, together with CZ gates between mirrored qubits.
