Quantum Circuit Simulation with Fast Tensor Decision Diagram

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 37x over Google's Tensor-Network library on redundancy-rich circuits, and 25x and 144x 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.