Tensor Decision Diagrams (TDDs) provide an efficient structure for representing tensors by combining techniques from both tensor networks and decision diagrams, demonstrating competitive performance in quantum circuit simulation and verification. However, existing decision diagrams, including TDDs, fail to exploit isomorphisms within tensors, limiting their compression efficiency. This paper introduces Local Invertible Map Tensor Decision Diagrams (LimTDDs), an extension of TDD that integrates local invertible maps (LIMs) to achieve more compact representations. Unlike LIMDD, which applies Pauli operators to quantum states, LimTDD generalizes this approach using the XP-stabilizer group, enabling broader applicability. We develop efficient algorithms for normalization and key tensor operations, including slicing, addition, and contraction, essential for quantum circuit simulation and verification. Theoretical analysis shows that LimTDD surpasses TDD in compactness while maintaining its generality and offers exponential advantages over both TDD and LIMDD in the best-case scenarios. Experimental results validate these improvements, demonstrating LimTDD's superior efficiency in quantum circuit simulation and functionality computation.

翻译：张量决策图（TDDs）通过结合张量网络和决策图的技术，为表示张量提供了一种高效结构，在量子电路模拟与验证中展现出具有竞争力的性能。然而，现有决策图（包括TDDs）未能利用张量内部的同构性，限制了其压缩效率。本文提出局部可逆映射张量决策图（LimTDDs），这是TDD的一种扩展，通过集成局部可逆映射（LIMs）以实现更紧凑的表示。与LIMDD将泡利算子应用于量子态不同，LimTDD利用XP稳定子群推广了该方法，从而具有更广泛的适用性。我们开发了用于归一化及关键张量操作（包括切片、加法与缩并）的高效算法，这些操作对量子电路模拟与验证至关重要。理论分析表明，LimTDD在保持通用性的同时，其紧凑性优于TDD，并且在最佳情况下相对于TDD和LIMDD均具有指数级优势。实验结果验证了这些改进，证明了LimTDD在量子电路模拟与功能计算方面具有更优的效率。