Gradient-based reconstruction of molecular Hamiltonians and density matrices from time-dependent quantum observables

Abstract

We consider a quantum system with a time-independent Hamiltonian parametrized by a set of unknown parameters $\alpha$. 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 $\mathcal{O}(t)$. We show that it is possible to obtain closed-form expressions for the gradients of the distance between $\mathcal{O}(t)$ and a calculated observable with respect to $\alpha$, $P$ 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 $\alpha$, $P$ 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.

References in corpus (3)

• Visualizing molecular unidirectional rotation
• Bayesian optimization for inverse problems in time-dependent quantum dynamics
• Echoes in Unidirectionally Rotating Molecules

Cited by in corpus (1)

• Topology identification of autonomous quantum dynamical networks