Li Hao-En, Li Xiang, Huang Jia-Cheng, Zhang Guang-Ze, Shen Zhu-Ping, Zhao Chen, Li Jun, Hu Han-Shi
Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China.
Department of Chemistry and Guangdong Provincial Key Laboratory of Catalytic Chemistry, Southern University of Science and Technology, Shenzhen 518055, China.
J Chem Phys. 2024 Oct 14;161(14). doi: 10.1063/5.0228731.
The matrix product state (MPS) Ansatz offers a promising approach for finding the ground state of molecular Hamiltonians and solving quantum chemistry problems. Building on this concept, the proposed technique of quantum circuit MPS (QCMPS) enables the simulation of chemical systems using a relatively small number of qubits. In this study, we enhance the optimization performance of the QCMPS Ansatz by employing the variational quantum imaginary time evolution (VarQITE) approach. Guided by McLachlan's variational principle, the VarQITE method provides analytical metrics and gradients, resulting in improved convergence efficiency and robustness of the QCMPS. We validate these improvements numerically through simulations of H2, H4, and LiH molecules. In addition, given that VarQITE is applicable to non-Hermitian Hamiltonians, we evaluate its effectiveness in preparing the ground state of transcorrelated Hamiltonians. This approach yields energy estimates comparable to the complete basis set (CBS) limit while using even fewer qubits. In particular, we perform simulations of the beryllium atom and LiH molecule using only three qubits, maintaining high fidelity with the CBS ground state energy of these systems. This qubit reduction is achieved through the combined advantages of both the QCMPS Ansatz and transcorrelation. Our findings demonstrate the potential practicality of this quantum chemistry algorithm on near-term quantum devices.
矩阵乘积态（MPS）近似为寻找分子哈密顿量的基态和解决量子化学问题提供了一种很有前景的方法。基于这一概念，所提出的量子电路MPS（QCMPS）技术能够使用相对较少的量子比特来模拟化学系统。在本研究中，我们通过采用变分量子虚时演化（VarQITE）方法来提高QCMPS近似的优化性能。在麦克拉克伦变分原理的指导下，VarQITE方法提供了解析度量和梯度，从而提高了QCMPS的收敛效率和鲁棒性。我们通过对H2、H4和LiH分子的模拟从数值上验证了这些改进。此外，鉴于VarQITE适用于非厄米哈密顿量，我们评估了它在制备转相关哈密顿量基态方面的有效性。这种方法在使用更少量子比特的情况下产生的能量估计与完备基组（CBS）极限相当。特别是，我们仅使用三个量子比特对铍原子和LiH分子进行了模拟，与这些系统的CBS基态能量保持了高保真度。这种量子比特数量的减少是通过QCMPS近似和转相关的综合优势实现的。我们的研究结果证明了这种量子化学算法在近期量子设备上的潜在实用性。
