标题： 基于分子点群对称性的量子退火器上的电子结构理论 显示英文标题

标题： Electronic Structure Theory with Molecular Point Group Symmetries on Quantum Annealers

摘要： 量子计算有可能通过显著加快计算时间并指数级减少计算资源来彻底改变量子化学。 在这里，我们将基于全布尔对称群 $\mathbb{Z}_2^k$ 的对称适应的Jordan-Wigner编码与我们对Xia-Bian-Kais（XBK）方法的新实现相结合，以提高在量子退火器上电子结构理论计算的效率，特别是通过减少达到相同精度所需的量子位数量。 通过提供比之前工作更广泛的对称适应编码（SAE），我们能够模拟比之前报道的使用为量子退火器开发的方法且不使用活性空间研究的分子更大的分子。 我们计算了 H$_2$、LiH、He$_2$、H$_2$O、O$_2$、N$_2$、Li$_2$、F$_2$、CO、BH$_3$、NH$_3$以及 CH$_4$的势能面，在 STO-6G 基组中最大的分子使用我们的 SAE 需要 16 个量子比特，并与全组态相互作用结果进行了比较。 将SAE应用于XBK方法可使希尔伯特空间的大小呈指数级减少，并且随着问题规模的增大而表现良好。 对于决定XBK方法中哈密顿量嵌入所使用的辅助量子比特数量的关键变分参数的偶数值或大值，或者对于某些分子如He$_2$和H$_2$O，它不会引入显著的额外误差。 我们对此行为进行了解释，并对我们的方法的使用提出了建议。 显示英文摘要

摘要： Quantum computation has the potential to revolutionize quantum chemistry through major speedups to computation times and exponential reduction of computational resources. Here, we combine the symmetry-adapted Jordan-Wigner encoding based on the full Boolean symmetry group $\mathbb{Z}_2^k$ with our new implementation of the Xia-Bian-Kais (XBK) method for improving the efficiency of electronic structure theory calculations on quantum annealers, particularly by reducing the number of qubits needed to achieve the same accuracy. By providing a more extensive symmetry-adapted encoding (SAE) than previous work, we are able to simulate molecules larger than those previously reported that have been studied using methods developed for quantum annealers and without using an active space. We calculated the potential energy surfaces of H$_2$, LiH, He$_2$, H$_2$O, O$_2$, N$_2$, Li$_2$, F$_2$, CO, BH$_3$, NH$_3$, and CH$_4$, with the largest molecule in the STO-6G basis set requiring 16 qubits with our SAE, and compared them with full configuration interaction results. The application of SAE to the XBK method provides an exponential reduction of the size of the Hilbert space and scales well with the size of the problem. It does not introduce significant additional errors for even or large values of a key variational parameter that determines the number of ancilla qubits used in the XBK method's Hamiltonian embedding, or for certain molecules such as He$_2$ and H$_2$O. We provide an explanation for this behavior and a recommendation on the usage of our method.