To detect errors, we periodically measure X and Z parities of adjacent clusters of data qubits with the aid of d 2 − 1 measure qubits interspersed throughout the lattice. As shown in Fig. 1b, each ...

for error-corrected surface code logical qubits 3,4,13. Here d is the code distance indicating 2d 2 − 1 physical qubits used per logical qubit; p and ε d are the ...