论文标题
基于梯度的分子哈密顿量和密度矩阵的基于梯度的重建。
Gradient-based reconstruction of molecular Hamiltonians and density matrices from time-dependent quantum observables
论文作者
论文摘要
我们考虑了一个量子系统，该系统具有与一组未知参数$α$的参数为独立的哈密顿量。该系统是由一个依赖一组未知参数$ p $的进化操作员以一般量子状态制备的。准备后，系统会随着时间的推移而演变，并且其特征是与时间有关的可观察到$ {\ cal o}（t）$。我们表明，有可能获得$ {\ cal o}（t）$之间距离梯度的封闭形式表达式，并且对于$α$，$ p $，可观察到的计算出的可观察到的封闭式表达式以及系统密度矩阵的所有元素，无论是纯状态还是混合状态。这些梯度可用于预测梯度下降中，以推断$α$，$ p $以及动态可观察物的相关密度矩阵。我们将这种方法与随机相波函数近似结合在一起，以获得梯度的闭合形式表达式，这些梯度可用于从平均时间依赖的时间依赖性可观察物中推断出大量参与动力学的量子状态的问题。通过从激光诱导的时间依赖性分子比对来确定分子气（最初在室温下的热平衡中）的温度来说明该方法。
We consider a quantum system with a time-independent Hamiltonian parametrized by a set of unknown parameters $α$. The system is prepared in a general quantum state by an evolution operator that depends on a set of unknown parameters $P$. After the preparation, the system evolves in time, and it is characterized by a time-dependent observable ${\cal O}(t)$. We show that it is possible to obtain closed-form expressions for the gradients of the distance between ${\cal O}(t)$ and a calculated observable with respect to $α$, $P$ and all elements of the system density matrix, whether for pure or mixed states. These gradients can be used in projected gradient descent to infer $α$, $P$ and the relevant density matrix from dynamical observables. We combine this approach with random phase wave function approximation to obtain closed-form expressions for gradients that can be used to infer population distributions from averaged time-dependent observables in problems with a large number of quantum states participating in dynamics. The approach is illustrated by determining the temperature of molecular gas (initially, in thermal equilibrium at room temperature) from the laser-induced time-dependent molecular alignment.
