树宽作为基于张量网络的量子模拟的一个实用组件的基准测试
Benchmarking treewidth as a practical component of tensor-network--based quantum simulation
摘要：
张量网络是一种强大的因子分解技术，它可以减少对主要量子多体系统和算法进行数值模拟的资源需求。张量网络模拟的计算复杂性取决于张量秩和它们收缩的顺序。不幸的是，计算最佳收缩序列（排序）一般是一个计算困难（NP完全）的任务。在2005年，马尔可夫和施证明了最优收缩序列对应于张量网络的线图的最优（最小宽度）树分解，将收缩序列问题与结构图论中的丰富文献联系起来。虽然基于树宽的方法在很大程度上被忽略，有利于在以前的张量网络文献中的特定于类的算法，我们证明了它们的实际相关性所产生的问题，从两个不同的方法在量子模拟：多尺度纠缠重正化anomalization（MERA）数据集和量子电路所产生的量子近似优化算法（QAOA）。我们展示了多个制度，基于树宽的算法优于特定领域的算法，同时表明，算法的最佳选择有一个复杂的依赖于网络密度，预期收缩的复杂性，和用户运行时间的要求。我们进一步提供了一个开源软件框架，设计重点是可访问性和可扩展性，使可复制的实验评估和未来的探索竞争的方法由从业者。
英文摘要：
Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on the tensor ranks and the order in which they are contracted. Unfortunately, computing optimal contraction sequences (orderings) in general is known to be a computationally difficult (NP-complete) task. In 2005, Markov and Shi showed that optimal contraction sequences correspond to optimal (minimum width) tree decompositions of a tensor network's line graph, relating the contraction sequence problem to a rich literature in structural graph theory. While treewidth-based methods have largely been ignored in favor of dataset-specific algorithms in the prior tensor networks literature, we demonstrate their practical relevance for problems arising from two distinct methods used in quantum simulation: multi-scale entanglement renormalization ansatz (MERA) datasets and quantum circuits generated by the quantum approximate optimization algorithm (QAOA). We exhibit multiple regimes where treewidth-based algorithms outperform domain-specific algorithms, while demonstrating that the optimal choice of algorithm has a complex dependence on the network density, expected contraction complexity, and user run time requirements. We further provide an open source software framework designed with an emphasis on accessibility and extendability, enabling replicable experimental evaluations and future exploration of competing methods by practitioners.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
