Abstract
The realization of fault-tolerant quantum computers hinges on effective quantum error correction (QEC) protocols, whose performance significantly relies on the nature of the underlying noise. In this work, we directly study the structure of non-Markovian correlated errors and their impact on surface code memory performance. Specifically, we compare surface code performance under non-Markovian noise and independent circuit-level noise, while keeping marginal error rates constant. Our analysis shows that while not all temporally correlated structures are detrimental, certain structures, particularly multi-time 'streaky' correlations affecting syndrome qubits and two-qubit gates, can severely degrade logical error rate scaling. Furthermore, we discuss our results in the context of recent QEC experiments on physical devices. These findings underscore the importance of understanding and mitigating non-Markovian noise toward achieving practical, fault-tolerant quantum computing.