Designing selective thermal absorbers with factorization machines with quantum annealing

Quantum annealing (QA) is a heuristic optimization method for efficiently solving complex combinatorial problems with discrete variables. Thus, quantum annealing is proper for optical designs with multiple materials. The possible designs with multiple materials and various geometries form a huge solution space that is challenging for optimization. Due to their wave-like behavior, optical systems are typically coupled over long distances and can interfere with one another. Mathematically, this leads to high-order couplings in quantum annealing that are not supported by current quantum hardware. Factorization machines (FMs) can reduce high-order terms and provide an effective quadratic form suitable for quantum hardware. In this work, we adopt the previously proposed factorization machines with quantum annealing (FMQA) to design selective thermal absorbers. The FQMA, consisting of iterations between QA and FMs, has many hyperparameters, such as the initial inputs, latent factors, and selection of trained data. We study how these hyperparameters improve the convergence of the FMQA. We find that a balance between the initial random samplings and the sampling by QA is crucial for optimization. The principle underlying the entire optimization process of the FMQA requires a deliberate balance between depth and breadth, alongside an adiabatic approach. We design selective thermal absorbers to only absorb light with wavelengths ranging from 8 to 13 microns. We design the absorbers with silicon dioxide, PMMA, and silver. The FMQA with the optimized hyperparameters shows stably better figures of merit.