Neural Quantum Propagators for Driven-Dissipative Quantum Dynamics

TL;DR

This work introduces Neural Quantum Propagators (NQP), a universal neural operator framework for driven-dissipative quantum dynamics that learns propagators in Liouville space to advance density operators under time-dependent driving. By treating external fields as inputs to a Fourier-based neural operator, NQP achieves long-time predictions with arbitrary initial states and can transfer to systems governed by different Hamiltonians via a composition property of propagators. The physics-informed training combines data-driven propagation losses with residuals from the quantum master equation, enabling accurate dynamics for open quantum systems such as the spin-boson model and a three-state Gamma system. The approach offers a path toward efficient, transferable simulations of driven open quantum systems, though scaling to large many-body systems remains a challenge, potentially addressable via tensor-network representations or alternative learning strategies for control applications.

Abstract

Describing the dynamics of strong-laser driven open quantum systems is a very challenging task that requires the solution of highly involved equations of motion. While machine learning techniques are being applied with some success to simulate the time evolution of individual quantum states, their use to approximate time-dependent operators (that can evolve various states) remains largely unexplored. In this work, we develop driven neural quantum propagators (NQP), a universal neural network framework that solves driven-dissipative quantum dynamics by approximating propagators rather than wavefunctions or density matrices. NQP can handle arbitrary initial quantum states, adapt to various external fields, and simulate long-time dynamics, even when trained on far shorter time windows. Furthermore, by appropriately configuring the external fields, our trained NQP can be transferred to systems governed by different Hamiltonians. We demonstrate the effectiveness of our approach by studying the spin-boson and the three-state transition Gamma models.

Figures (4)

• Figure 1: The architecture of (a) the driven NQP model, and (b) the $l$-th Fourier layer, respectively. $\mathcal{F}$ and $\mathcal{F}^{-1}$ denote the Fourier transform and its inverse. $+$ and $\sigma$ are the element-wise addition and the GeLU activation function.
• Figure 2: The population and coherence dynamics of the spin-boson model at $\omega_{f} =$ (a) $0.2$, (b) $0.4$, (c) $0.6$, and (d) $1.0$ as predicted by the NQP model. The red, blue, green, and purple curves represent the populations, $p_{g}$, $p_{e}$, and the real and imaginary parts of $\rho_{eg}$, respectively. The solid and dashed lines represent the results from the NQP model and the reference RK4 (shown with a marker for better illustration), respectively.
• Figure 3: The population dynamics of the three-state system at $c_1 = 0.3$ and different $c_3$ cases. The solid line represents the results evaluated from our NQP model, which was shared among all the cases. The dotted line represents the reference RK4 result.
• Figure 4: The population dynamics $p_{g}(t)$ for different $\omega_{f}$ evaluated from the NQP model with $t_{max} = 5$ (red) and $10$ (blue). The reference RK4 results are shown in black.