Tensor networks represent the state-of-the-art in computational methods
across many disciplines, including the classical simulation of quantum
many-body systems and quantum circuits. Several applications of current
interest give rise to tensor networks with irregular geometries. Finding the
best possible contraction path for such networks is a central problem, with an
exponential effect on computation time and memory footprint. In this work, we
implement new randomized protocols that find very high quality contraction
paths for arbitrary and large tensor networks. We test our methods on a variety
of benchmarks, including the random quantum circuit instances recently
implemented on Google quantum chips. We find that the paths obtained can be
very close to optimal, and often many orders or magnitude better than the most
established approaches. As different underlying geometries suit different
methods, we also introduce a hyper-optimization approach, where both the method
applied and its algorithmic parameters are tuned during the path finding. The
increase in quality of contraction schemes found has significant practical
implications for the simulation of quantum many-body systems and particularly
for the benchmarking of new quantum chips. Concretely, we estimate a speed-up
of over 10,000$\times$ compared to the original expectation for the classical
simulation of the Sycamore `supremacy' circuits.

本研究提出了一种新的随机协议，通过超优化方法，在任意大的张量网络中找到最优的收缩路径，这对于模拟量子多体系统以及量子芯片测试的速度提升具有重要的实际意义。