The successful operation of quantum computers relies on protecting qubits from decoherence and noise, which-if uncorrected-will lead to erroneous results. Because these errors accumulate during an algorithm, correcting them is a key requirement for large-scale and fault-tolerant quantum information processors. Besides computational errors, which can be addressed by quantum error correction1-9, the carrier of the information can also be completely lost or the information can leak out of the computational space10-14. It is expected that such loss errors will occur at rates that are comparable to those of computational errors. Here we experimentally implement a full cycle of qubit loss detection and correction on a minimal instance of a topological surface code15,16 in a trapped-ion quantum processor. The key technique used for this correction is a quantum non-demolition measurement performed via an ancillary qubit, which acts as a minimally invasive probe that detects absent qubits while imparting the smallest quantum mechanically possible disturbance to the remaining qubits. Upon detecting qubit loss, a recovery procedure is triggered in real time that maps the logical information onto a new encoding on the remaining qubits. Although the current demonstration is performed in a trapped-ion quantum processor17, the protocol is applicable to other quantum computing architectures and error correcting codes, including leading two- and three-dimensional topological codes. These deterministic methods provide a complete toolbox for the correction of qubit loss that, together with techniques that mitigate computational errors, constitute the building blocks of complete and scalable quantum error correction.

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量子比特损失的实验确定性校正

量子计算机的成功运行依赖于保护量子位免受退相干和噪声的影响，如果不加以纠正，将会导致错误的结果。由于这些错误在算法过程中会累积，因此纠正它们是大规模和容错量子信息处理器的关键要求。除了可以通过量子纠错1-9解决的计算错误之外，信息的载体也可能完全丢失或信息可能泄漏出计算空间10-14。预计这种损失错误的发生率与计算错误的发生率相当。在这里，我们在俘获离子量子处理器中的拓扑表面代码的最小实例上实验性地实现了一个完整的量子位丢失检测和校正周期15,16。用于这种校正的关键技术是通过辅助量子位执行的量子非破坏测量，它充当微创探针，检测不存在的量子位，同时对剩余的量子位施加最小的量子力学可能干扰。在检测到量子位丢失后，实时触发恢复过程，将逻辑信息映射到剩余量子位的新编码上。虽然目前的演示是在俘获离子量子处理器中进行的，但该协议适用于其他量子计算架构和纠错码，包括领先的二维和三维拓扑代码。这些确定性方法为纠正量子比特损失提供了一个完整的工具箱，连同减少计算错误的技术，