Low-overhead surface code logical Hadamard

Understand

We present an improved low-overhead implementation of surface code logical H.

• We describe in full detail logical H applied to a single distance 7 double-defect logical qubit in an otherwise idle scalable array such qubits.
• Our goal is to provide a clear description of logical H and to emphasize that the surface code possesses low-overhead implementations of the entire Clifford group.