论文标题
轨道优化变分量子质量的二阶导数的分析公式：适用于极化性
Analytical formulation of the second-order derivative of energy for orbital-optimized variational quantum eigensolver: application to polarizability
论文作者
论文摘要
我们开发了一种量子古典杂化算法来计算轨道优化的变量变量量子eigensolver（OO-VQE）的能量的分析二阶导数，这是一种计算给定分子大麻的特征素化的方法，该方法是利用近端量子计算机和类别计算机计算的给定分子的方法。我们表明，可以在量子计算机上评估算法中所需的所有数量，以作为标准的量子期望值评估，而无需使用任何辅助量子A。我们通过对量子电路的数值模拟来验证我们的公式，以计算水分子的极化性，这是能量相对于电场的二阶导数。此外，将噻吩和呋喃分子的极化和折射率计算为可能的工业应用测试台。我们最终分析了通过提出的分析衍生物获得的估计极化的误差缩放与有限差异获得的数值。数值计算表明，我们的分析衍生物比量子计算机上的测量值（运行）少于数值导数才能达到相同的固定精度。
We develop a quantum-classical hybrid algorithm to calculate the analytical second-order derivative of the energy for the orbital-optimized variational quantum eigensolver (OO-VQE), which is a method to calculate eigenenergies of a given molecular Hamiltonian by utilizing near-term quantum computers and classical computers. We show that all quantities required in the algorithm to calculate the derivative can be evaluated on quantum computers as standard quantum expectation values without using any ancillary qubits. We validate our formula by numerical simulations of quantum circuits for computing the polarizability of the water molecule, which is the second-order derivative of the energy with respect to the electric field. Moreover, the polarizabilities and refractive indices of thiophene and furan molecules are calculated as a testbed for possible industrial applications. We finally analyze the error-scaling of the estimated polarizabilities obtained by the proposed analytical derivative versus the numerical one obtained by the finite difference. Numerical calculations suggest that our analytical derivative requires fewer measurements (runs) on quantum computers than the numerical derivative to achieve the same fixed accuracy.
