Fan Yi, Liu Jie, Li Zhenyu, Yang Jinlong
Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China.
Hefei National Laboratory, University of Science and Technology of China, Hefei, Anhui 230088, China.
J Chem Theory Comput. 2023 Aug 22;19(16):5407-5417. doi: 10.1021/acs.jctc.3c00068. Epub 2023 Jul 28.
As demonstrated in the density matrix renormalization group (DMRG) method, approximating many-body wave function of electrons using a matrix product state (MPS) is a promising way to solve electronic structure problems. The expressibility of an MPS is determined by the size of the matrices or, in other words, the bond dimension, which unfortunately may be required to be very large in quantum chemistry simulations. In this study, we propose to calculate the ground state energies of molecular systems by variationally optimizing quantum circuit MPS (QCMPS) with a relatively small number of qubits. It is demonstrated that with carefully chosen circuit structure and orbital localization scheme, QCMPS can reach a similar accuracy as that achieved in DMRG with an exponentially large bond dimension. QCMPS simulation of a linear hydrogen molecular chain with 50 orbitals can reach the chemical accuracy using only 6 qubits at a moderate circuit depth. These results suggest that QCMPS is a promising wave function ansatz in the variational quantum eigensolver algorithm for molecular systems.
正如在密度矩阵重整化群（DMRG）方法中所展示的那样，使用矩阵乘积态（MPS）来近似电子的多体波函数是解决电子结构问题的一种很有前景的方法。MPS的可表达性由矩阵的大小决定，或者换句话说，由键维度决定，不幸的是，在量子化学模拟中可能需要非常大的键维度。在本研究中，我们提议通过变分优化具有相对较少量子比特数的量子电路MPS（QCMPS）来计算分子体系的基态能量。结果表明，通过精心选择电路结构和轨道定域化方案，QCMPS可以达到与具有指数级大键维度的DMRG所达到的精度相似的精度。对具有50个轨道的线性氢分子链进行QCMPS模拟，在适度的电路深度下仅使用6个量子比特就能达到化学精度。这些结果表明，QCMPS在分子体系的变分量子本征求解器算法中是一种很有前景的波函数假设。
