标题： 矩阵乘积算子和树张量网络算子的最优符号构造 显示英文标题

标题： Optimal Symbolic Construction of Matrix Product Operators and Tree Tensor Network Operators

摘要： 这项研究引入了一种改进的框架，用于构建矩阵乘积算子（MPO）和树张量网络算子（TTNO），这些是量子模拟中的关键工具。 给定的（哈密顿）算子通常具有已知的符号“算子字符串之和”形式，可以转换为张量网络结构。 结合现有的基于二分图的方法和一种新引入的符号高斯消元预处理步骤，我们提出的方法在哈密顿项具有相同系数的情况下优于早期算法。 我们通过与现有方法进行比较来测试我们方法的性能。 最后，我们将我们的方法应用于溶剂中分子填充腔体的模型。 这个开放量子系统被转化为层次运动方程（HEOM）设置，以获得有效的哈密顿量。 相应TTNO的构建展示了最大键维数的次线性增长。 显示英文摘要

摘要： This research introduces an improved framework for constructing matrix product operators (MPOs) and tree tensor network operators (TTNOs), crucial tools in quantum simulations. A given (Hamiltonian) operator typically has a known symbolic "sum of operator strings" form that can be translated into a tensor network structure. Combining the existing bipartite-graph-based approach and a newly introduced symbolic Gaussian elimination preprocessing step, our proposed method improves upon earlier algorithms in cases when Hamiltonian terms share the same prefactors. We test the performance of our method against established ones for benchmarking purposes. Finally, we apply our methodology to the model of a cavity filled with molecules in a solvent. This open quantum system is cast into the hierarchical equation of motion (HEOM) setting to obtain an effective Hamiltonian. Construction of the corresponding TTNO demonstrates a sub-linear increase of the maximum bond dimension.