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arXiv · 2503.22061

$\texttt{Symdyn}$: an automated algebraic solution for high-order quantum systems

D. Martínez-Tibaduiza·Vladimir Vargas-Calderón·J. G. Dueñas·J. Flórez-Jiménez·A. Z. Khoury
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Abstract

Many significant quantum physical systems are characterized by Hamiltonians expressible as a linear combination of time-independent generators of a closed Lie algebra, $\hat{H}(t)=\sum_{l=1}^{L}\eta_{l}(t)\hat{g}_{l}$. The Wei-Norman method provides a framework for determining the coefficients of the corresponding time evolution operator in its factorized representation, $\hat{U}(t) = \prod_{l=1}^{L} e^{ \Lambda_{l}(t)\hat{g}_{l}}$. This work introduces $\texttt{Symdyn}$, a Python library that automates the application of this method. The library efficiently computes similarity transformations and the nonlinear differential equations intrinsic to derive Baker-Campbell-Hausdorff-like relations and the time evolution of high-order quantum systems ($L\geq 6$). We demonstrate its robustness by deriving the time evolution operator for a system of two time-dependent coupled harmonic oscillators. Additionally, we specialize the library to the Lie group $\textit{SU}(N)$, showing its versatility with $\textit{SU}(2)$, $\textit{SU}(3)$ and $\textit{SU}(4)$ examples, relevant to quantum computing.

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D. Martínez-Tibaduiza, Vladimir Vargas-Calderón, J. G. Dueñas, J. Flórez-Jiménez, A. Z. Khoury. 2025-03-28. $\texttt{Symdyn}$: an automated algebraic solution for high-order quantum systems. https://doi.org/10.1103/24r3-j9zy

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