Fig. 6: Flag-based QEC with ququarts.
From: An architecture for two-qubit encoding in neutral ytterbium-171 atoms
a Circuit to fault-tolerantly extract the stabilizer XXXX. Black lines are data qubits and yellow and red lines are syndrome and flag qubits encoded in a ququart. The CNOTs between syndrome and flag qubits are performed with intra-ququart gates, which should suppress the infidelity to the same level as single-qubit gates. b Simulated threshold for ⟦5, 1, 3⟧ and Steane ⟦7, 1, 3⟧ codes. Circles represent normal flag EC and triangles represent flag EC with ququart by assuming intra-ququart gates have perfect fidelity. The intersection of the gray line (physical error rate) and the curve representing logical error rate of a certain case gives the physical error rate, below which the QEC code outperforms the bare qubit. Using a ququart flag improves the threshold, and in practice, the threshold should lie in between the normal flag case and the ququart flag case.
