Hyper-optimized tensor network contraction

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