.png){kind=icon}
返回
Differentiable Programming Tensor Networks
.png){kind=icon}
OA
AI
DOI：10.1103/PhysRevX.9.031041.png)
.png){kind=icon}
.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
Differentiable programming is a fresh programming paradigm which composes parameterized algorithmic components and optimizes them using gradient search. The concept emerges from deep learning but is not limited to training neural networks. We present the theory and practice of programming tensor network algorithms in a fully differentiable way. By formulating the tensor network algorithm as a computation graph, one can compute higher-order derivatives of the program accurately and efficiently using automatic differentiation. We present essential techniques to differentiate through the tensor networks contraction algorithms, including numerical stable differentiation for tensor decompositions and efficient backpropagation through fixed-point iterations. As a demonstration, we compute the specific heat of the Ising model directly by taking the second-order derivative of the free energy obtained in the tensor renorrnalization group calculation. Next, we perform gradient-based variational optimization of infinite projected entangled pair states for the quantum antiferromagnetic Heisenberg model and obtain state-of-the-art variational energy and magnetization with moderate efforts. Differentiable programming removes laborious human efforts in deriving and implementing analytical gradients for tensor network programs, which opens the door to more innovations in tensor network algorithms and applications.
Keyword:
MATRIX RENORMALIZATION-GROUP
AUTOMATIC DIFFERENTIATION
QUANTUM COMPUTATION
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
IF:
15.7
论文数:
2.7K
被引数:
3.4W
机构
引用论文
Infinite projected entangled pair states algorithm improved: Fast full update and gauge fixing.png)
PHYSICAL REVIEW BOAAI
PHYSICAL REVIEW BIF3.7
OAAI分享收藏Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS studyPHYSICAL REVIEW BOAAI
PHYSICAL REVIEW BIF3.7
OAAI分享收藏
查看更多内容