基于轨道优化VQE与误差缓解的量子硬件上的解析核梯度与 Hessian 矩阵
Analytical Nuclear Gradients and Hessians on Quantum Hardware via Orbital-Optimized VQE with Error Mitigation
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中文总结 AI 辅助
本研究提出结合轨道优化与线性响应理论的方法，在量子硬件上实现核梯度与 Hessian 矩阵的解析计算，通过误差缓解方案校正期望值，经氢、水分子验证，明确误差来源并指明改进方向。
中文摘要 AI 辅助
核梯度与 Hessian 矩阵是计算化学中的基础量，对几何优化、振动光谱及分子性质计算等广泛应用至关重要。本研究在量子硬件上实现了这两个量的解析计算方法，该方法在活性空间框架内结合了轨道优化与线性响应理论。在量子计算端，该方法采用 tiled 幺正乘积态（tUPS）拟设直接计算求解响应方程所需的张量元；此外，采用适配的混淆矩阵误差缓解方案结合后选择准则对期望值进行校正。通过计算氢分子和水分子的势能面、核梯度、Hessian 矩阵及振动频率，评估了该工作流的能力与当前局限性。结果显示氢分子的性能良好，而水分子对量子硬件资源提出了更高要求，凸显了误差缓解策略的权衡。对结果的量化分析明确了主要误差来源，为更精准的量子计算机应用指明了改进方向。
英文摘要
Nuclear gradients and Hessians are fundamental quantities in computational chemistry, essential for a wide range of applications including geometry optimization, vibrational spectroscopy, and molecular property calculations. In this work, we present their analytical implementation on quantum hardware. The methodology is formulated within an active-space framework combining orbital optimization and linear-response theory. On the quantum-computing side, the approach employs the tiled unitary product state (tUPS) ansatz to directly evaluate the tensor elements required for solving the response equations. Moreover, the expectation values are corrected using an adapted confusion-matrix error-mitigation scheme in combination with post-selection criteria. The resulting workflow is assessed on molecular hydrogen and on water through the calculation of potential energy surfaces, nuclear gradients, Hessians, and vibrational frequencies, enabling the evaluation of both its capabilities and current limitations. The results demonstrate good performance for the hydrogen molecule, whereas the water molecule provides a more demanding test of quantum-hardware resources and highlights the trade-offs associated with error-mitigation strategies. The quantified analysis of the results identify the main sources of errors, suggesting improvement directions for more accurate quantum computer applications.
