Benchmarking the optimization of optical machines with the planted solutions

This research focuses on developing effective benchmarks for quadratic unconstrained binary optimization instances, crucial for evaluating the performance of Ising hardware and solvers. Currently, the field lacks accessible and reproducible models for systematically testing such systems, particularly in terms of detailed phase space characterization. Here, we introduce universal generative models based on an extension of Hebb’s rule of associative memory with asymmetric pattern weights. We conduct comprehensive calculations across different scales and dynamical equations, examining outcomes like the probabilities of reaching the ground state, planted state, spurious state, or other energy levels. Additionally, the generated problems reveal properties such as the easy-hard-easy complexity transition and complex solution cluster structures. This method offers a promising platform for analyzing and understanding the behavior of physical hardware and its simulations, contributing to future advancements in optimization technologies.