Yoshikawa Takeshi, Takanashi Tomoya, Nakai Hiromi
Faculty of Pharmaceutical Sciences, Toho University, 2-2-1 Miyama, Funabashi, Chiba 274-8510, Japan.
Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan.
J Chem Theory Comput. 2022 Sep 13;18(9):5360-5373. doi: 10.1021/acs.jctc.2c00602. Epub 2022 Aug 4.
The variational quantum eigensolver (VQE) with shallow or constant-depth quantum circuits is one of the most pursued approaches in the noisy intermediate-scale quantum (NISQ) devices with incoherent errors. In this study, the divide-and-conquer (DC) linear scaling technique, which divides the entire system into several fragments, is applied to the VQE algorithm based on the unitary coupled cluster (UCC) method, denoted as DC-qUCC/VQE, to reduce the number of required qubits. The unitarity of the UCC ansatz that enables the evaluation of the total energy as well as various molecular properties as expectation values can be easily implemented on quantum devices because the quantum gates are unitary operators themselves. Based on this feature, the present DC-qUCC/VQE algorithm is designed to conserve the total number of electrons in the entire system using the density matrix evaluated on a quantum computer. Numerical assessments clarified that the energy errors of the DC-qUCC/VQE calculations decrease by using the constraint of the total number of electrons. Furthermore, the DC-qUCC/VQE algorithm could reduce the number of quantum gates and shows the possibility of decreasing incoherent errors.
具有浅量子电路或常深度量子电路的变分量子本征求解器（VQE）是在存在非相干误差的噪声中等规模量子（NISQ）设备中最受追捧的方法之一。在本研究中，将整个系统划分为几个片段的分治（DC）线性缩放技术应用于基于幺正耦合簇（UCC）方法的VQE算法，记为DC-qUCC/VQE，以减少所需量子比特的数量。UCC近似的幺正性使得能够将总能量以及各种分子性质作为期望值进行评估，这可以在量子设备上轻松实现，因为量子门本身就是幺正算符。基于这一特性，当前的DC-qUCC/VQE算法旨在利用在量子计算机上评估的密度矩阵来守恒整个系统中的电子总数。数值评估表明，通过使用电子总数的约束，DC-qUCC/VQE计算的能量误差会减小。此外，DC-qUCC/VQE算法可以减少量子门的数量，并显示出减少非相干误差的可能性。
