发表机构
Singapore University of Technology and Design (SUTD)（新加坡科技设计大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出CT-bMPS，一种基于收缩树边界矩阵乘积态的近似张量网络收缩方法，通过局部压缩和环境更新实现高效计算，并在多个基准测试中展现优于现有方法的准确性和可扩展性。
AI 中文摘要
我们引入了收缩树边界矩阵乘积态（CT-bMPS），这是一种用于一般闭合张量网络的可扩展近似收缩方法。CT-bMPS将收缩树每条边上的边界张量及其互补环境表示为矩阵乘积态。这种表示允许基于约化转移矩阵进行局部压缩，以沿任意收缩树纳入环境信息，同时保持时间和内存成本在网络规模和键维上呈多项式增长。我们在多种模型和应用上对该方法进行了基准测试，包括伊辛配分函数、随机张量网络、踢伊辛动力学和量子纠错解码。这些基准测试表明，与现有的通用近似收缩方法相比，该方法在准确性和计算效率上均有提升，并且能够处理更大、更复杂的网络。优化的收缩树和环境更新在不增加键维的情况下显著提高了准确性。这些结果确立了CT-bMPS作为一个通用且可扩展的近似框架，具有灵活的收缩顺序和基于环境的压缩，适用于广泛的应用。
英文摘要
We introduce contraction tree boundary matrix product states (CT-bMPS), a scalable approximate contraction method for general closed tensor networks. CT-bMPS represents the boundary tensor and its complementary environment at each edge of a contraction tree as matrix product states. This representation allows local compression based on a reduced transition matrix to incorporate environment information along arbitrary contraction trees, while keeping the time and memory costs polynomial in the network size and bond dimension. We benchmark the method on a variety of models and applications, including Ising partition functions, random tensor networks, kicked Ising dynamics, and quantum error correction decoding. These benchmarks demonstrate improved accuracy and computational efficiency over existing general-purpose approximate contraction methods, together with the ability to handle larger and more complex networks. Optimized contraction trees and environment updates substantially improve accuracy without increasing the bond dimension. These results establish CT-bMPS as a general and scalable approximation framework with flexible contraction orders and environment-based compression for a wide range of applications.
Comments20 pages, 12 figures
