Parallel tensor network contraction algorithms have emerged as the pivotal benchmarks for assessing the classical limits of computation, exemplified by Google's demonstration of quantum supremacy through random circuit sampling. However, the massive parallelization of the algorithm makes it vulnerable to computer node failures. In this work, we apply coded computing to a practical parallel tensor network contraction algorithm. To the best of our knowledge, this is the first attempt to code tensor network contractions. Inspired by matrix multiplication codes, we provide two coding schemes: 2-node code for practicality in quantum simulation and hyperedge code for generality. Our 2-node code successfully achieves significant gain for $f$-resilient number compared to naive replication, proportional to both the number of node failures and the dimension product of sliced indices. Our hyperedge code can cover tensor networks out of the scope of quantum, with degraded gain in the exchange of its generality.

翻译：并行张量网络缩并算法已成为评估经典计算极限的关键基准，例如谷歌通过随机电路采样演示量子优越性的工作。然而，该算法的大规模并行化使其易受计算节点故障的影响。在本工作中，我们将编码计算应用于一种实用的并行张量网络缩并算法。据我们所知，这是对张量网络缩并进行编码的首次尝试。受矩阵乘法编码的启发，我们提出了两种编码方案：面向量子模拟实用性的2节点编码，以及面向通用性的超边编码。我们的2节点编码相比朴素复制方案，在$f$容错节点数上成功实现了显著增益，该增益与节点故障数量及切片索引维度乘积均成正比。我们的超边编码能够覆盖量子领域之外的张量网络，其通用性是以增益降低为代价实现的。