Papers › Symdyn: an automated algebraic solution for high-order quantum systems
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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Many significant quantum physical systems are characterized by Hamiltonians expressible as a linear combination of time-independent generators of a closed Lie algebra, Ĥ(t)=∑ₗ₌₁ᴸηₗ(t)ĝₗ. The Wei-Norman method provides a framework for determining the coefficients of the corresponding time evolution operator in its factorized representation, Û(t) = ∏ₗ₌₁ᴸ e^(Λₗ(t)ĝₗ). This work introduces 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≥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 SU(N), showing its versatility with SU(2), SU(3) and SU(4) examples, relevant to quantum computing.
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