Massive Parallel Simulation for Tensor Network Contraction Ordering Solving

Tensor network contraction is a powerful mathematical tool for dealing with complex systems and high-dimensional data, which is widely used in classical simulations of molecules and quantum circuits. To improve the performance of simulations, existing methods are implemented by searching the optimal contraction orderings for tensor networks. In particular, some reinforcement learning (RL) methods show a greater potential for solving. However, with the increasing scale of simulation, the number of tensors in the corresponding tensor network is huge, the existing RL methods suffer from sampling bottlenecks and slow solving speed, which make it difficult to efficiently solve for high-quality contraction orderings. In this paper, we design a massive parallel simulation environment for tensor network contraction ordering solving on a single GPU. We experimented with multiple numbers of parallel environments on the tensor-train network, and achieved the highest speedup when the number of environments was 2
⁶
. We also have experimented on large-scale tensor-train networks and tree tensor networks, and compared to Kahypar and RL-Baseline, our method achieves average speedup of 8.96× and 7.48× on tensor-train networks, and 10.03× and 7.48× on tree tensor networks.