用DMRG优化张量网络，让量子态表示更准确
Quantum Tensor Network Learning with DMRG
- 引入全局归一化条件，使矩阵乘积态表示量子态
- 对比梯度下降与DMRG方法，发现后者在优化上更有效
- 适合量子计算与复杂系统建模的研究者参考
张量网络是一种相对较新的机器学习方法，其架构最初受量子多体物理模拟启发。常见的结构是矩阵乘积态（MPS），也称为张量列车，通常通过梯度下降进行优化。本文引入全局归一化条件，使MPS能够表示量子态。研究了两种优化方法：一种基于梯度下降，另一种基于对密度矩阵重整化群（DMRG）的改编，比较了它们在寻找局部最优张量方面的有效性。
原文摘要 · Abstract (English)
Tensor Networks are a relatively new machine learning approach. The architectures proposed initially are inspired by approaches from quantum many-body physics simulations. One common layout is the matrix product state (MPS) also known as a tensor train optimized with gradient descent techniques. We introduce a global normalization condition, so that the MPS represents a quantum state. We investigate two optimization methods that find the locally optimal tensors and compare them regarding their effectiveness. One is based on gradient descent and the other on an adaptation of DMRG.
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