在态平均轨道优化变分量子本征求解器内的解析非绝热耦合与梯度
Analytical nonadiabatic couplings and gradients within the state-averaged orbital-optimized variational quantum eigensolver
AI总结：
本文对SA-OO-VQE算法进行技术与解析扩展，提出高效态分辨过程并实现解析梯度和非绝热耦合估计，在甲亚胺分子上验证了准确性并定位了圆锥交叉。
摘要：
在这项工作中，我们对最近的态平均轨道优化变分量子本征求解器（SA-OO-VQE）算法（参见文献[S. Yalouz et al., Quantum Sci. Technol. 6, 024004 (2021).]）引入了若干技术和解析扩展。受当前量子计算机的局限性所驱动，第一个扩展在于一种高效的态分辨过程，用于寻找SA-OO-VQE本征态，而不仅仅是它们所张成的子空间，同时保持在等权系综框架内。这种方法通过将此问题推迟到整个算法的最后，避免了昂贵的中间本征态分辨。第二个扩展允许估计解析梯度和非绝热耦合，这在许多实际情况中至关重要，从搜索圆锥交叉到模拟量子动力学，例如在光异构化反应中。我们新实现的准确性在甲亚胺分子CH$_2$NH（一种与研究较大生物分子中光异构化相关的最小席夫碱模型）上得到了证明，为此我们还进行了几何优化，以定位该分子基态与第一激发电子态之间的圆锥交叉。
英文摘要：
In this work, we introduce several technical and analytical extensions to our recent state-averaged orbital-optimized variational quantum eigensolver (SA-OO-VQE) algorithm (see Ref. [S. Yalouz et al. ,Quantum Sci. Technol. 6, 024004 (2021).]). Motivated by the limitations of current quantum computers, the first extension consists in an efficient state-resolution procedure to find the SA-OO-VQE eigenstates, and not just the subspace spanned by them, while remaining in the equi-ensemble framework. This approach avoids expensive intermediate resolutions of the eigenstates by postponing this problem to the very end of the full algorithm. The second extension allows for the estimation of analytical gradients and non-adiabatic couplings, which are crucial in many practical situations ranging from the search of conical intersections to the simulation of quantum dynamics, in, for example, photoisomerization reactions. The accuracy of our new implementations is demonstrated on the formaldimine molecule CH$_2$NH (a minimal Schiff base model relevant for the study of photoisomerization in larger bio-molecules), for which we also perform a geometry optimization to locate a conical intersection between the ground and first-excited electronic states of the molecule.
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