Theory of analytical energy derivatives for the variational quantum eigensolver
Theory of analytical energy derivatives for the variational quantum eigensolver
复制标题
变分量子本征解的解析能量导数理论
DOI：
10.1103/physrevresearch.2.013129
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发表时间：
2020-02-05
影响因子：
4.2
通讯作者：
Mizukami, Wataru
中科院分区：
文献类型：
--
作者：
Mitarai, Kosuke;Nakagawa, Yuya O.;Mizukami, Wataru
变分量子本征求解器（VQE）及其变体是一种寻找给定哈密顿量的本征态和本征能量的方法，是近期量子计算机的重要应用。虽然本征能确实是决定给定系统性质的重要量，但它们对系统参数的导数，如原子核的位置，如果我们以量子化学问题为目标，对分析系统也是至关重要的。在这里，我们描述了在VQE框架中计算给定哈密顿量的特征能量的解析导数的方法，包括激发态能量和基态能量，相对于系统参数。我们给出了显式的低深度量子电路，它可以测量必要的量来评估能量导数，并结合了原理证明的数值模拟。这项工作扩展了变分量子本征求解器的理论，使其能够测量量子系统比以前更多的物理性质，并探索化学反应。
The variational quantum eigensolver (VQE) and its variants, which is a method for finding eigenstates and eigenenergies of a given Hamiltonian, are appealing applications of near-term quantum computers. Although the eigenenergies are certainly important quantities which determine properties of a given system, their derivatives with respect to parameters of the system, such as positions of nuclei if we target a quantum chemistry problem, are also crucial to analyze the system. Here, we describe methods to evaluate analytical derivatives of the eigenenergy of a given Hamiltonian, including the excited state energy as well as the ground-state energy, with respect to the system parameters in the framework of the VQE. We give explicit, low-depth quantum circuits which can measure essential quantities to evaluate energy derivatives, incorporating with proof-of-principle numerical simulations. This work extends the theory of the variational quantum eigensolver, by enabling it to measure more physical properties of a quantum system than before and to explore chemical reactions.