Quantum circuit simulation is a challenging computational problem crucial for quantum computing research and development. The predominant approaches in this area center on tensor networks, prized for their better concurrency and less computation than methods using full quantum vectors and matrices. However, even with the advantages, array-based tensors can have significant redundancy. We present a novel open-source framework that harnesses tensor decision diagrams to eliminate overheads and achieve significant speedups over prior approaches. On average, it delivers a speedup of 37$\times$ over Google's TensorNetwork library on redundancy-rich circuits, and 25$\times$ and 144$\times$ over quantum multi-valued decision diagram and prior tensor decision diagram implementation, respectively, on Google random quantum circuits. To achieve this, we introduce a new linear-complexity rank simplification algorithm, Tetris, and edge-centric data structures for recursive tensor decision diagram operations. Additionally, we explore the efficacy of tensor network contraction ordering and optimizations from binary decision diagrams.

翻译：量子电路模拟是量子计算研发中具有挑战性的关键计算问题。当前主流方法以张量网络为核心，相比使用完整量子向量与矩阵的方法，其具有更好的并发性与更低的计算量。然而，即便具备这些优势，基于数组的张量仍存在显著的冗余性。我们提出了一种新颖的开源框架，通过利用张量决策图消除计算开销，相较于先前方法实现了显著的加速效果。在冗余丰富的电路上，该框架平均比Google TensorNetwork库快37倍；在Google随机量子电路上，比量子多值决策图和先前张量决策图实现分别快25倍和144倍。为实现这一目标，我们引入了新型线性复杂度秩简化算法Tetris，以及用于递归张量决策图操作的边中心数据结构。此外，我们还探究了张量网络收缩排序与二元决策图优化策略的有效性。