Fig. 1: A fault-tolerant circuit to make parity measurements.
From: Encoding a magic state with beyond break-even fidelity
a, A circuit that measures SX, SZ and \(\overline{W}\) using flag qubits on the heavy-hexagonal lattice architecture. b, The four-qubit code is encoded on qubits with even indices and the other qubits are used to make the fault-tolerant parity measurement. The circuit measures SX by setting \(U={\mathbb{1}}\) and SZ by setting U = H, where H is the Hadamard gate. The circuit measures \(\overline{W}\) if we set U = T. The measurement outcome M gives the reading of the parity measurement. Essential to the fault-tolerant procedure are flag fault-tolerant readout circuits4,5,27,51 that identify errors that occur during the parity measurement. Outcomes f and g are flag qubit readings that indicate that the circuit may have introduced a logical error to the data qubits.
