AI 中文总结
研究针对投影纠缠对态变分优化中能量梯度评估的计算瓶颈与数值不稳定问题，采用隐式微分技术，通过重新表述核心步骤、选择合适参数化来降低成本、消除不稳定，简化了基于梯度的稳定PEPS优化实现。
AI 中文摘要
当前对投影纠缠对态（PEPS）进行变分优化的主要方法基于自动微分，这便于评估相对于局部变分自由度的能量梯度。然而，能量梯度评估不仅仍是优化过程的主要计算瓶颈，还常遭遇数值不稳定性。在这项工作中，我们采用隐式微分技术的最新进展来应对PEPS优化中的这些挑战。通过根据收缩环境的单个特征方程重新表述梯度计算的核心步骤，降低了梯度计算成本并改善了其与问题规模的缩放关系。基于收缩环境的内在对称性选择合适的特征方程参数化，可直接消除全局梯度计算中因收缩算法子程序导数产生的不稳定性。最后，我们展示了该方法如何极大简化基于梯度的稳定PEPS优化的实际实现。
英文摘要
The current leading approach to the variational optimization of projected entangled-pair states (PEPS) is based on automatic differentiation, which allows for a convenient evaluation of the energy gradient with respect to the local variational degrees of freedom. However, evaluating the energy gradient not only remains a major computational bottleneck of the optimization procedure, but also suffers from frequent numerical instabilities. In this work, we adopt recent advances in implicit differentiation techniques to address these challenges in PEPS optimization. By reformulating the core step of the gradient computation in terms of a single characteristic equation for the contraction environment, we reduce the cost of the gradient computation and improve its scaling with the problem size. By choosing a suitable parametrization of this characteristic equation based on the intrinsic symmetries of the contraction environment, we can directly remove instabilities from the global gradient computation that would otherwise arise from the derivatives of subroutines of the contraction algorithm. Finally, we demonstrate how this approach drastically simplifies the practical implementation of stable gradient-based PEPS optimization.
