The accurate calculation of electronic potential energy surfaces for ground and excited states is crucial for understanding photochemical processes, particularly near conical intersections. While classical methods are limited by scaling and quantum algorithms by hardware, this thesis focuses on the State-Averaged Orbital-Optimized Variational Quantum Eigensolver (SA-OO-VQE). This hybrid quantum-classical algorithm provides a balanced description of multiple electronic states by combining quantum state preparation with classical state-averaged orbital optimization. A key contribution is the implementation and evaluation of the Differential Evolution algorithm within the SA-OO-VQE framework, with a comparative study against classical optimizers like the Broyden-Fletcher-Goldfarb-Shanno (BFGS) and Sequential Least Squares Programming (SLSQP) algorithms. The performance of these optimizers is assessed by calculating ground and first excited state energies for H$_2$, H$_4$, and LiH. The thesis also demonstrates SA-OO-VQE's capability to accurately model potential energy surfaces near conical intersections, using formaldimine as a case study. The results show that orbital optimization is essential for correctly capturing the potential energy surface topology, a task where standard methods with fixed orbitals fail. Our findings indicate that while Differential Evolution presents efficiency challenges, gradient-based methods like BFGS and SLSQP offer superior performance, confirming that the SA-OO-VQE approach is crucial for treating complex electronic structures.

翻译：精确计算基态和激发态的电子势能面对于理解光化学过程至关重要，尤其是在锥形交叉附近。虽然经典方法受限于标度问题，而量子算法受限于硬件，本论文聚焦于状态平均轨道优化变分量子本征求解器（SA-OO-VQE）。这种混合量子-经典算法通过结合量子态制备与经典的状态平均轨道优化，为多个电子态提供了平衡的描述。一个关键贡献是在SA-OO-VQE框架内实现并评估了差分进化算法，并与经典优化器如Broyden-Fletcher-Goldfarb-Shanno（BFGS）和序列最小二乘规划（SLSQP）算法进行了比较研究。通过计算H$_2$、H$_4$和LiH的基态和第一激发态能量，评估了这些优化器的性能。本论文还以甲亚胺为案例，展示了SA-OO-VQE在锥形交叉附近精确模拟势能面的能力。结果表明，轨道优化对于正确捕捉势能面拓扑结构至关重要，而使用固定轨道的标准方法在此任务上会失败。我们的发现表明，尽管差分进化算法存在效率挑战，但基于梯度的方法如BFGS和SLSQP提供了更优的性能，证实了SA-OO-VQE方法对于处理复杂电子结构至关重要。