AI 中文总结
研究如何将哈密顿量和成本函数的符号描述转换为MPO表示，核心方法是利用autotn软件，通过自动机启发方法识别重复模式构建紧凑张量网络表示，主要贡献是减少了开发、验证和比较MPO构建的工程工作量。
AI 中文摘要
矩阵乘积算子（MPO）是张量网络模拟和量子计算应用中结构化算子的标准表示。然而，将哈密顿量和成本函数的符号描述转换为MPO表示通常需要大量手动实现，易出错且难以重现。本文提出了autotn，一个将符号算子规则转换为MPO表示的开源Python软件工具。用户以高级格式定义局部算子和相互作用规则，软件生成相应MPO及验证工具。它采用自动机启发方法，识别算子符号描述中的重复模式并重用构建紧凑张量网络表示，避免手工构建每个张量。当前实现支持组合优化问题中常见的对角算子以及量子多体物理中的一般局部矩阵算子。软件在最大割成本算子、长程XX + YY + Z自旋哈密顿量和量子时钟模型上进行了演示。通过提供从符号模型规范到经过验证的MPO构建的可重现工作流程，autotn减少了开发、验证和比较MPO构建所需的工程工作量。
英文摘要
Matrix product operators (MPOs) are a standard representation for structured operators in tensor-network simulations and quantum computing applications. However, converting symbolic descriptions of Hamiltonians and cost functions into MPO representations often requires substantial manual implementation, making the process error-prone and difficult to reproduce. This paper presents autotn, an open-source Python software tool that converts symbolic operator rules into MPO representations. Users define local operators and interaction rules in a high-level format, and the software generates the corresponding MPO along with validation utilities. In doing so, the software follows an automata-inspired approach that identifies repeated patterns in the symbolic description of the operator and reuses them to build a compact tensor-network representation, avoiding the need to construct each tensor by hand. The current implementation of autotn supports both diagonal operators, commonly encountered in combinatorial optimization problems, and general local matrix operators used in quantum many-body physics. The software is demonstrated on Max-Cut cost operators, long-range XX+YY+Z spin Hamiltonians, and quantum clock models. By providing a reproducible workflow from symbolic model specification to validated MPO construction, autotn reduces the engineering effort required to develop, verify, and compare MPO constructions.
Comments19 pages, 4 figures. Submitted to SoftwareX
