One of the key problems in tensor network based quantum circuit simulation is the construction of a contraction tree which minimizes the cost of the simulation, where the cost can be expressed in the number of operations as a proxy for the simulation running time. This same problem arises in a variety of application areas, such as combinatorial scientific computing, marginalization in probabilistic graphical models, and solving constraint satisfaction problems. In this paper, we reduce the computationally hard portion of this problem to one of graph linear ordering, and demonstrate how existing approaches in this area can be utilized to achieve results up to several orders of magnitude better than existing state of the art methods for the same running time. To do so, we introduce a novel polynomial time algorithm for constructing an optimal contraction tree from a given order. Furthermore, we introduce a fast and high quality linear ordering solver, and demonstrate its applicability as a heuristic for providing orderings for contraction trees. Finally, we compare our solver with competing methods for constructing contraction trees in quantum circuit simulation on a collection of randomly generated Quantum Approximate Optimization Algorithm Max Cut circuits and show that our method achieves superior results on a majority of tested quantum circuits. Reproducibility: Our source code and data are available at https://github.com/cameton/HPEC2022_ContractionTrees.

翻译：以电磁网络为基础的量子电路模拟的关键问题之一是构建一个缩缩树,以最大限度地降低模拟的成本,其成本可以以操作数量表示,作为模拟运行时间的替代。同样的问题也出现在多个应用领域,例如组合科学计算、概率图形模型中的边缘化和解决约束性满意度问题。在本文中,我们将这一问题的计算硬部分降低到图形线性订单中,并展示如何利用这个区域的现有方法达到比当前工艺水平更好的几个数量级的结果。为了做到这一点,我们采用了一种新型的多元时间算法,用于从给定的顺序中构建最佳的收缩树。此外,我们引入了一个快速和高质量的线性订单求解器,并证明它作为向收缩树提供订单的灵敏性。最后,我们将我们的解答器与在量电路模拟中构建收缩树的竞合方法相比较,以随机生成的Qantum Aprimical Algoritoimal, Max Cutrical-produbilations 和显示我们的方法在亚氏度/Restibrevaral上实现了高端点。