基于 MindQuantum 的量子变分求解器拟设研究

从费曼提出量子计算设想到量子计算优越性的验证，量子计算已经取得了许 多重大进步。在量子计算的热潮中，量子化学研究遇见了新的机遇。其中著名的量 子变分求解算法（Variational quantum eigensolver, VQE）在带噪声的中等规模量子 计算（Noisy intermediate-scale quantum, NISQ）时代得到了广泛关注。与量子相位 估计算法（Quantum phase estimation, QPE）相比，VQE 算法降低了对相干时间的 要求，代价是需要重复测量待求解哈密顿量的期望值。在 VQE 算法的流程中，需 要先将带参数的量子线路作用在初始态上作为试验态（拟设），接着用经典优化算 法去调节参数来降低待求解哈密顿量的期望值，最终可以求解得到哈密顿量的基态。

在 VQE 算法中，拟设的设计方式对问题的求解至关重要。其中幺正耦合簇 （Unitary coupled cluster, UCC）拟设最早提出并且在实验上完成了验证。然而当模 拟规模增加时，现有的量子硬件系统无法提供实现该拟设所需的量子资源。基于 量子硬件条件硬件友好型拟设（Hardware-efficient ansatz, HEA）结构容易实现却不 一定使得能量收敛最快。针对上述问题，论文中研究了受启发于上述两种拟设的 新拟设，称为对称的硬件友好型拟设（Symmetric hardware-efficient ansatz, SHEA）。 它在原来泡利演化算符对应量子线路的基础上引入了额外了的参数来增加其表达 性。SHEA 拟设有重复结构和变结构两种类型。对 LiH，BeH2 分子在 STO-3G 基 组下的数值模拟中证明重复结构的 SHEA 拟设在精度和收敛稳定性上要优于 HEA 拟设。在对 H4 分子的数值模拟中，采用预筛选策略构建的变结构 SHEA 拟设的线 路更加简洁高效。相信 SHEA 拟设的研究将会为量子化学模拟提供新的思路。

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