用机器学习从量子实验数据中自动还原出高维时空几何。
Machine-learning emergent spacetime from linear response in future tabletop quantum gravity experiments
- 用神经网络处理量子系统线性响应数据，实现全息对偶下的高维时空重建。
- 通过新设计的龙格-库塔层提升数值精度，成功让引力度规作为可解释权重自动涌现。
- 为未来桌面量子引力实验提供可落地的重建方法，适合理论物理与实验交叉研究者。
我们提出一种新型可解释神经网络模型，用于在反德西特/共形场论（AdS/CFT）对偶框架下实现高精度体空间重构。根据该对偶关系，环状凝聚态系统在全息意义上等价于体空间上的引力系统，使得桌面量子引力实验成为可能（如 arXiv:2211.13863 所述）。本文旨在利用机器学习，从凝聚态系统数据中重构更高维度的引力度规。我们的神经网络读取凝聚态系统时空非均匀的线性响应数据，并引入一种新型层，实现龙格-库塔方法以获得更好的数值控制。结果表明，通过监督学习，该模型可自动将高维引力度规作为可解释的权重涌现出来。所提出的算法可作为通用体空间重构的基础，为实现阿德斯/共形场论对偶提供实际解决方案，并将在未来的桌面量子引力实验中部署。
原文摘要 · Abstract (English)
We introduce a novel interpretable Neural Network (NN) model designed to perform precision bulk reconstruction under the AdS/CFT correspondence. According to the correspondence, a specific condensed matter system on a ring is holographically equivalent to a gravitational system on a bulk disk, through which tabletop quantum gravity experiments may be possible as reported in arXiv:2211.13863. The purpose of this paper is to reconstruct a higher-dimensional gravity metric from the condensed matter system data via machine learning using the NN. Our machine reads spatially and temporarily inhomogeneous linear response data of the condensed matter system, and incorporates a novel layer that implements the Runge-Kutta method to achieve better numerical control. We confirm that our machine can let a higher-dimensional gravity metric be automatically emergent as its interpretable weights, using a linear response of the condensed matter system as data, through supervised machine learning. The developed method could serve as a foundation for generic bulk reconstruction, i.e., a practical solution to the AdS/CFT correspondence, and would be implemented in future tabletop quantum gravity experiments.
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