Potts model solver based on hybrid physical and digital architecture

• Published in: Communications physics 2022-05, Vol.5 (1), p.1-8, Article 137
• Main Authors: Inaba, Kensuke, Inagaki, Takahiro, Igarashi, Koji, Utsunomiya, Shoko, Honjo, Toshimori, Ikuta, Takuya, Enbutsu, Koji, Umeki, Takeshi, Kasahara, Ryoichi, Inoue, Kyo, Yamamoto, Yoshihisa, Takesue, Hiroki
• Format: Article
• Language: English
• Subjects: 639/766/25; 639/766/400/385; Clustering; Digital computers; Graph coloring; Integers; Ising model; Iterative methods; Learning; Optical Parametric Oscillators; Optimization; Parametric amplifiers; Physics; Physics and Astronomy; Solvers
• ISSN: 2399-3650; 2399-3650
• DOI: 10.1038/s42005-022-00908-0

The Potts model describes Ising-model-like interacting spin systems with multivalued spin components, and ground-state search problems of the Potts model can be efficiently mapped onto various integer optimization problems thanks to the rich expression of the multivalued spins. Here, we demonstrate a solver of this model based on hybrid computation using physical and digital architectures, wherein a digital computer updates the interaction matrices in the iterative calculations of the physical Ising-model solvers. This update of interactions corresponds to learning from the Ising solutions, which allows us to save resources when embedding a problem in a physical system. We experimentally solved integer optimization problems (graph coloring and graph clustering) with this hybrid architecture in which the physical solver consisted of coupled degenerate optical parametric oscillators. Hybrid computing seeks to divide operations based on the strengths of digital, analogue or physical architectures. Here, approximate solutions to the multi-state Potts model are found using a physical Ising solver, networked degenerate optical parametric oscillators, repeatedly with learning processes.