Fault-tolerant threshold of quantum circuit under correlated noise

Abstract We investigate the impact of the correlation between error gates on the fault-tolerant threshold in quantum circuits under three typical noise models. In the fault-tolerant encoding schemes for two fundamental quantum logical operations, we extend the conventional error injection method by simultaneously applying error gates to both control and target qubits after two-qubit gate operations, with a quantitative characterization of the correlation strength between these error gates. The results show that the fault-tolerant error threshold can be noticeably enhanced by the presence of correlations between error gates, resulting in more robust quantum circuit implementations. We further apply fault-tolerant encoding to the single-qubit teleportation circuit and investigate the effect of correlated noise on its error threshold. The results show that the threshold varies non-monotonically with the correlation strength and that the system’s fault-tolerance differs significantly across noise models.