标题： 变分子空间方法及其在改进变分蒙特卡罗动力学中的应用 显示英文标题

标题： Variational subspace methods and application to improving variational Monte Carlo dynamics

摘要： 我们提出了一种形式化方法，允许直接操作和优化子空间，从而避免在使用子空间方法时优化单个状态的需要。 通过行列式状态映射，我们可以自然地将距离和能量等概念扩展到子空间，以及蒙特卡洛估计器，从而恢复了Pfau等人提出的激发态估计方法。 作为实际应用，我们随后介绍了Bridge，这是一种通过提取变分时间演化状态的线性组合来提高变分动力学性能的方法。 我们发现Bridge在计算上成本低廉，并且能够显著减轻由于动力学离散化而产生的误差，因此可以系统地用作变分动力学的后处理工具。 显示英文摘要

摘要： We present a formalism that allows for the direct manipulation and optimization of subspaces, circumventing the need to optimize individual states when using subspace methods. Using the determinant state mapping, we can naturally extend notions such as distance and energy to subspaces, as well as Monte Carlo estimators, recovering the excited states estimation method proposed by Pfau et al. As a practical application, we then introduce Bridge, a method that improves the performance of variational dynamics by extracting linear combinations of variational time-evolved states. We find that Bridge is both computationally inexpensive and capable of significantly mitigating the errors that arise from discretizing the dynamics, and can thus be systematically used as a post-processing tool for variational dynamics.