Limitations of tensor-network approaches for optimization and sampling: A comparison to quantum and classical Ising machines

In the ever-evolving landscape of computational science, tensor networks have emerged as a versatile toolset to simulate both quantum and classical many-body systems. This study investigates their applicability to complex optimization problems, where quantum annealing devices have generated significant interest. A challenge in applying tensor networks here is the high connectivity of the devices, which this work effectively leverages by utilizing sparse structures in construction, plus hardware acceleration. The authors quantify the limitations of their deterministic approach, and find that in certain scenarios it might outperform quantum annealers or randomized classical solvers.