更高效的软输出解码：额外簇增长与早停
Even More Efficient Soft-Output Decoding with Extra-Cluster Growth and Early Stopping
AI总结：
本文提出两种新型软输出方法，通过早停技术降低计算复杂度，提高FPGA解码器的硬件兼容性。
摘要：
在容错量子计算中，实时解码器的软输出在提高解码准确性、后选魔态和加速晶格手术中起着关键作用。Meister等人[arXiv:2405.07433 (2024)]最近提出了一种高效方法来评估基于簇的解码器的软输出，包括并查集（UF）解码器。然而，在并行计算环境中，其计算复杂度与或甚至超过UF解码器本身，导致显著的开销。此外，该方法需要解码图的全局信息，使其不适合现有在场可编程门阵列（FPGA）上的UF解码器硬件实现。在本文中，为缓解这些问题，我们开发了更高效的评估基于簇的解码器高质量软输出的方法，引入了几种早停技术。我们的核心思想是，大软输出的精确值在实践中往往并不必要。基于这一见解，我们引入了两种新型软输出：有界簇间隙和额外簇间隙。前者通过在早期阶段终止计算来降低Meister方法的计算复杂度。我们的数值模拟显示，该方法在代码距离d方面相比原始提案实现了改进的扩展性。后者，额外簇间隙，通过解码器获得的簇进行小幅度的额外增长来量化解码器可靠性。这种方法提供了显著的优势，即在不修改现有FPGA实现的UF解码器架构的情况下实现软输出计算。这些技术提供了更低的计算复杂度和更高的硬件兼容性，为未来具有软输出的实时解码器奠定了关键基础。
英文摘要：
In fault-tolerant quantum computing, soft outputs from real-time decoders play a crucial role in improving decoding accuracy, post-selecting magic states, and accelerating lattice surgery. A recent paper by Meister et al. [arXiv:2405.07433 (2024)] proposed an efficient method to evaluate soft outputs for cluster-based decoders, including the Union-Find (UF) decoder. However, in parallel computing environments, its computational complexity is comparable to or even surpasses that of the UF decoder itself, resulting in a substantial overhead. Furthermore, this method requires global information about the decoding graph, making it poorly suited for existing hardware implementations of the UF decoder on Field-Programmable Gate Arrays (FPGAs). In this paper, to alleviate these issues, we develop more efficient methods for evaluating high-quality soft outputs in cluster-based decoders by introducing several early-stopping techniques. Our central idea is that the precise value of a large soft output is often unnecessary in practice. Based on this insight, we introduce two types of novel soft-outputs: the bounded cluster gap and the extra-cluster gap. The former reduces the computational complexity of Meister's method by terminating the calculation at an early stage. Our numerical simulations show that this method achieves improved scaling with code distance $d$ compared to the original proposal. The latter, the extra-cluster gap, quantifies decoder reliability by performing a small, additional growth of the clusters obtained by the decoder. This approach offers the significant advantage of enabling soft-output computation without modifying the existing architecture of FPGA-implemented UF decoders. These techniques offer lower computational complexity and higher hardware compatibility, laying a crucial foundation for future real-time decoders with soft outputs.
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