Simula­ted anneal­ing (e.g. quantum inspi­red Ising machi­nes, Fujitsu Digital Annea­ler, Evo Annealer)

Simula­ted Anneal­ing is a classi­cal optimiza­tion method in which combi­na­to­rial problems are formu­la­ted as Ising models or as Quadra­tic Uncons­trai­ned Binary Optimiza­tion (QUBO) problems and solved using a thermally inspi­red search dynamics. A control­led reduc­tion of an effec­tive tempe­ra­ture governs the transi­tion proba­bi­li­ties between states, thereby enabling the escape from local minima and the gradual approach to low‑energy soluti­ons. Quantum‑inspired Ising machi­nes imple­ment this anneal­ing princi­ple in entirely classi­cal hardware or software systems. Their quantum‑inspired charac­ter arises from the adoption of modeling and solution princi­ples from quantum optimiza­tion, without making use of physi­cal quantum effects. Examp­les include Fujitsu’s Digital Annea­ler as well as Evo Annealer–type approa­ches, which realize annealing‑like dynamics partly on specia­li­zed classi­cal hardware such as Field‑Programmable Gate arrays (FPGAs). Such systems serve both as powerful tools for indus­trial optimiza­tion problems and as metho­do­lo­gi­cal reference points and bridging techno­lo­gies for future quantum‑based optimiza­tion methods.