Despite large advances in both algorithms and computer technology, even typical instances of certain computationally hard problems (NP-hard) may be too difficult to be solved on today’s computers. In certain areas of application unconventional computational devices could help to overcome these limitations. This research project aims at **ultrafast analog simulations of classical spin systems** using a large-scale network of coupled photon Bose-Einstein condensates.

An important goal of this project is to use photon BEC networks as a tool for solving the ground-state energy problem (GSE) in the disordered XY model faster than any other computer today. The ground-state energy problem in XY spin glasses, which corresponds to finding the lowest energy state in a frustrated magnet, is a difficult combinatorial problem that is known to be NP-hard. The latter implies that every other NP problem can be mapped onto the GSE problem in XY spin glasses in polynomial time. A computer that solves the GSE problem, thus, solves the whole class of NP problems. That includes, for example, instances of the famous traveling salesman, graph coloring, and partitioning problem. A device that significantly speeds up such calculations would represent a tremendous breakthrough in computing.

**Key publications**

- D. Dung, C. Kurtscheid, T. Damm, J. Schmitt, F. Vewinger, M. Weitz, and J. Klaers, “Variable potentials for thermalized light and coupled condensates”,
*Nature Photonics***11**, 565 (2017). link