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Bulletin of the American Physical Society

Large-Scale Simulation of Quantum Circuits via Tensor Network Contraction

Cupjin Huang, Fang Zhang, Michael Newman, Junjie Cai, Xun Gao, Zhengxiong Tian, Junyin Wu, Haihong Xu, Huanjun Yu, Bo Yuan, Márió Szegedy, Yaoyun Shi, Jianxin Chen

Published Mar 16, 2021• 0 citations
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Tensor network contraction is a fundamental operation for dealing with high-dimensional data, which is now widely used in classical simulations of quantum circuits. To improve the performance of simulations, existing methods are implemented by optimizing contraction methods. However, with the increasing size of the tensor network, the contraction efficiency of these methods is difficult to satisfy the performance requirements and also suffers from the challenge of contracting tensor tasks that exceed GPU memory. In this paper, we propose a high-performance chunking method for tensor contraction. By chunking the given tensor, we obtain small tensors or vectors assign the corresponding threads, and contract them in parallel through the GPU. Solving high-order tensor contractions using distributed tensor contraction methods. Compared to the Einsum, our method achieves an average speedup of 22.28×. We also have experiments for large-scale tensor network contractions and our method achieves an average speedup of 13.56× compared to Tensordot.
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 26. 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.