Nakagawa Yuya O, Chen Jiabao, Sudo Shotaro, Ohnishi Yu-Ya, Mizukami Wataru
QunaSys Inc., Aqua Hakusan Building 9F, 1-13-7 Hakusan, Bunkyo, Tokyo 113-0001, Japan.
Materials Informatics Initiative, RD Technology and Digital Transformation Center, JSR Corporation, 3-103-9, Tonomachi, Kawasaki-ku, Kawasaki, Kanagawa 210-0821, Japan.
J Chem Theory Comput. 2023 Apr 11;19(7):1998-2009. doi: 10.1021/acs.jctc.2c01176. Epub 2023 Mar 28.
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 test bed for possible industrial applications. We finally analyze the error scaling of the estimated polarizabilities obtained by the proposed analytical derivative versus the numerical derivative 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.
我们开发了一种量子-经典混合算法，用于计算轨道优化变分量子本征求解器（OO-VQE）能量的解析二阶导数，OO-VQE是一种利用近期量子计算机和经典计算机来计算给定分子哈密顿量本征能量的方法。我们表明，该算法中计算导数所需的所有量都可以在量子计算机上作为标准量子期望值进行评估，而无需使用任何辅助量子比特。我们通过计算水分子极化率（即能量相对于电场的二阶导数）的量子电路数值模拟来验证我们的公式。此外，计算了噻吩和呋喃分子的极化率和折射率，作为可能的工业应用的测试平台。我们最后分析了所提出的解析导数得到的估计极化率与有限差分得到的数值导数的误差缩放情况。数值计算表明，与数值导数相比，我们的解析导数在量子计算机上达到相同固定精度所需的测量（运行）次数更少。
