2p-H-13 Simulated Annealing の Hubbard 模型への応用

Masaru Kato, Takashi Kitagaki

盛 猪苗代, 知行 深沢

青木 秀夫, 洗 上村

Rana Fareed Ghani

Simulated annealing (SA) has been considered as a good tool for searchand optimization problems which represent the abstraction of obtaining thecrystalline structure through a physical process. This algorithm works sequentiallythat the current state will produce only one next state. That will make the search tobe slower and the important drawback is that the search may fall in local minimumwhich represent the best solution in only part of the solution space. In this workwe present the transformation of Simulated Annealing algorithm into quantumversion which will be called Quantum Simulated Annealing (QSA). Thisalgorithm will overcome the drawbacks of slowness and local minimum falling byproduce as much as possible of the neighbor states and work on in parallel byexploiting the massive parallelism feature in quantum computation. The resultsshow that QSA can find the optimal path in smaller number of iterations than thesequential simulated annealing algorithm and the time complexity of QSA isbetter than any other parallel simulated annealing algorithm.

永生 大畠

Masaru Kato

We have developed a simulated-annealing method that is applicable for interacting fermion systems at finite temperature. We apply this method to the square Hubbard model of filling 0.8. From results of the simulation we find that the undulating-stripe spin-density wave (SDW) is most stable at low temperature. At increasing temperature, the stable state changes to stripe SDW, spiral SDW, N\'eel state, and paramagnetic state, successively.