Fig. 3

Surface-code stabiliser measurements in a segmented chain qubit array. a The lattice of the surface code. b The layout of two-qubit gates for measuring the first-row of X stabilisers. Circles are data qubits, and empty circles are unused data qubits in short columns. Squares are shuttle qubits, which are moved between nearest neighbouring columns as indicated by gray arrows. Black curves are CNOT gates. c Circuit of X-stabiliser measurements. d Circuit of Z-stabiliser measurements. Qubits 1, 2, 3 and 4 are data qubits, and other two qubits are shuttle qubits, which are initialised and measured in the circuit. The upper shuttle qubit is shared by segments of qubit-1 and qubit-2, and the lower shuttle qubit is shared by segments of qubit-3 and qubit-4. Qubit-2 and qubit-3 are in the same segment (column), which is a long column in c and a short column in d. The first CNOT gate prepares a Bell state on two shuttle qubits, which can be viewed as one qubit encoded in two qubits and prepared in the state either \(\left| 0 \right\rangle\) or \(\left| + \right\rangle\) depending on the code word. The encoded qubit plays exactly the same role as the only one ancillary qubit in usual statbiliser measurment cirucits.²⁶