Running quantum algorithms protected by quantum error correction requires a real time, classical decoder. To prevent the accumulation of a backlog, this decoder must process syndromes from the quantum device at a faster rate than they are generated. Most prior work on real time decoding has focused on an isolated logical qubit encoded in the surface code. However, for surface code, quantum programs of utility will require multi-qubit interactions performed via lattice surgery. A large merged patch can arise during lattice surgery -- possibly as large as the entire device. This puts a significant strain on a real time decoder, which must decode errors on this merged patch and maintain the level of fault-tolerance that it achieves on isolated logical qubits. These requirements are relaxed by using spatially parallel decoding, which can be accomplished by dividing the physical qubits on the device into multiple overlapping groups and assigning a decoder module to each. We refer to this approach as spatially parallel windows. While previous work has explored similar ideas, none have addressed system-specific considerations pertinent to the task or the constraints from using hardware accelerators. In this work, we demonstrate how to configure spatially parallel windows, so that the scheme (1) is compatible with hardware accelerators, (2) supports general lattice surgery operations, (3) maintains the fidelity of the logical qubits, and (4) meets the throughput requirement for real time decoding. Furthermore, our results reveal the importance of optimally choosing the buffer width to achieve a balance between accuracy and throughput -- a decision that should be influenced by the device's physical noise.

翻译：运行受量子纠错保护的量子算法需要一个实时的经典解码器。为了防止积压，该解码器必须以比量子设备生成更快的速度处理来自该设备的综合症。先前关于实时解码的大多数工作都集中在表面码编码的孤立逻辑量子比特上。然而，对于表面码，有实用价值的量子程序需要通过晶格手术执行多量子比特相互作用。在晶格手术期间可能出现一个大的合并补丁——可能大到覆盖整个设备。这对实时解码器造成了巨大压力，它必须解码此合并补丁上的错误，并维持在孤立逻辑量子比特上实现的容错水平。通过使用空间并行解码可以放松这些要求，这可以通过将设备上的物理量子比特划分为多个重叠组并为每个组分配一个解码器模块来实现。我们将这种方法称为空间并行窗口。虽然先前的工作已经探索了类似的想法，但都没有解决与该任务相关的系统特定考虑因素或使用硬件加速器带来的约束。在这项工作中，我们展示了如何配置空间并行窗口，以使该方案（1）与硬件加速器兼容，（2）支持通用的晶格手术操作，（3）保持逻辑量子比特的保真度，以及（4）满足实时解码的吞吐量要求。此外，我们的结果揭示了优化选择缓冲区宽度以在精度和吞吐量之间取得平衡的重要性——这一决策应受到设备物理噪声的影响。