在周期正方形和立方格子上,针对粗的能量-景观旋转镜的张量网络的超优化近似收缩
Adil A Gangat1,2, Johnnie Gray2
1Physics & Informatics Laboratories, NTT Research, Inc., Sunnyvale, California 94085, USA.
Physical review. E
|February 7, 2025
概括
这项研究扩展了张量网络方法,以找到平面几何之外的低能自旋玻璃配置. 该方法在复杂的能源环境中显示出有希望的准确性,有助于组合优化.
科学领域:
- 凝聚物质物理学 凝聚物质物理学
- 计算物理 计算物理
- 统计力学 统计力学
背景情况:
- 在旋转玻璃中找到低能量的配置对于组合优化和基本科学至关重要.
- 传统的搜索启发学与含有众多局部最小值的崎的能量景观作斗争.
- 张量网络收缩为采样博尔兹曼分布提供了一个有希望的替代方案,独立于平面几何形状的景观粗性.
研究的目的:
- 为了研究张量网络收缩方法的扩展,用于超越平面几何形状的旋转眼镜.
- 评估非平面旋转玻璃系统中超优化的近似张量网络收缩的有效性.
- 评估这种方法对各种格子类型和系统大小的计算复杂性和准确性.
主要方法:
- 利用了超优化的近似张量网络收缩.
- 在定期方形和立方格的Ising旋转玻璃上进行了测试,这些玻璃是通过种植瓦产生的.
- 分析了不同系统大小 (高达2304次旋转) 和键层尺寸的性能.
- 与最佳解决方案相比,测量的相对能量误差.
主要成果:
- 在最粗的实例中,以4的键位维度实现了~1% (方格格子) 和~10% (立方格子) 的平均相对能量误差.
- 为不那么坚固的实例找到最佳或接近最佳的解决方案.
- 对于一个固定债券维度的系统大小,证明了二次时间复杂性.
结论:
- 超优化的张量网络收缩对于平面几何之外的旋转眼镜是有效的.
- 这种方法提供了一条可行的途径,用于解决崎的能源景观中复杂的优化问题.
- 基于张量网络的优化的未来发展具有显著的潜力,超越了二进制和双体模型.
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