Low-Rank Matrices, NP-Hardness, and the Roadblocks to Quantum-Inspired Hardware

This article explores the intersection of graph theory, NP-complete problems, and hardware constraints in solving Ising models with optical annealers. It highlights how low-rank graph structures, mappings like the knapsack and scheduling problems, and precision limits shape computational hardness. Despite challenges in scaling, modified formulations such as constrained number partitioning offer adaptable testbeds for SPIM devices, balancing complexity with practical resource limits.