Leakage outside of the qubit computational subspace, present in many leading experimental platforms, constitutes a threatening error for quantum error correction (QEC) for qubits. We develop a leakage-detection scheme via Hidden Markov models (HMMs) for transmon-based implementations of the surface code. By performing realistic density-matrix simulations of the distance-3 surface code (Surface-17), we observe that leakage is sharply projected and leads to an increase in the surface-code defect probability of neighboring stabilizers. Together with the analog readout of the ancilla qubits, this increase enables the accurate detection of the time and location of leakage. We restore the logical error rate below the memory break-even point by post-selecting out leakage, discarding less than half of the data for the given noise parameters. Leakage detection via HMMs opens the prospect for near-term QEC demonstrations, targeted leakage reduction and leakage-aware decoding and is applicable to other experimental platforms.

在许多领先的实验平台中存在的量子位计算子空间外部泄漏，构成了量子位纠错（QEC）的威胁性错误。我们通过隐马尔可夫模型（HMM）开发了泄漏检测方案，用于基于Transmon的表面代码实现。通过执行距离3表面代码（Surface-17）的逼真的密度矩阵模拟，我们观察到泄漏被急剧投影，并导致相邻稳定器的表面代码缺陷概率增加。加上辅助位的模拟读数，这种增加可以准确检测泄漏的时间和位置。通过选择泄漏，我们将逻辑错误率恢复到低于存储器的收支平衡点，对于给定的噪声参数，丢弃少于一半的数据。