Ryabinkin Ilya G, Genin Scott N, Izmaylov Artur F
Department of Physical and Environmental Sciences , University of Toronto Scarborough , Toronto , Ontario M1C 1A4 , Canada.
Chemical Physics Theory Group, Department of Chemistry , University of Toronto , Toronto , Ontario M5S 3H6 , Canada.
J Chem Theory Comput. 2019 Jan 8;15(1):249-255. doi: 10.1021/acs.jctc.8b00943. Epub 2018 Dec 18.
Variational quantum eigensolver (VQE) is an efficient computational method promising chemical accuracy in electronic structure calculations on a universal-gate quantum computer. However, such a simple task as computing the electronic energy of a hydrogen molecular cation, H, is not possible for a general VQE protocol because the calculation will invariably collapse to a lower energy of the corresponding neutral form, H. The origin of the problem is that VQE effectively performs an unconstrained energy optimization in the Fock space of the original electronic problem. We show how this can be avoided by introducing necessary constraints directing VQE toward the electronic state of interest. The proposed constrained VQE can find an electronic state with a certain number of electrons, a certain spin, or any other property. Moreover, the new algorithm naturally removes unphysical kinks in potential energy surfaces (PESs), which frequently appeared in the regular VQE and required significant additional quantum resources for their removal. We demonstrate the performance of the constrained VQE by simulating PESs of various states of H and HO on Rigetti Computing Inc.'s 19Q-Acorn quantum processor.
变分量子本征求解器（VQE）是一种高效的计算方法，有望在通用门量子计算机上进行电子结构计算时达到化学精度。然而，对于一般的VQE协议来说，像计算氢分子阳离子H⁺的电子能量这样简单的任务是不可能完成的，因为计算总是会坍缩到相应中性形式H的较低能量。问题的根源在于，VQE在原始电子问题的福克空间中有效地执行了无约束能量优化。我们展示了如何通过引入必要的约束来引导VQE朝向感兴趣的电子态，从而避免这个问题。所提出的约束VQE可以找到具有特定电子数、特定自旋或任何其他性质的电子态。此外，新算法自然地消除了势能面（PES）中经常出现在常规VQE中且需要大量额外量子资源才能消除的非物理扭结。我们通过在Rigetti Computing Inc.的19Q-Acorn量子处理器上模拟H⁺和H₂O各种态的PES来展示约束VQE的性能。
