AI 中文总结
该研究针对电子结构哈密顿量的第一量子化基态能量估计，采用平方和谱隙放大协议，识别哈密顿量的平方和表示，改进块编码归一化，降低资源估计，实现渐近门复杂度提升。
AI 中文摘要
我们通过采用平方和谱隙放大协议，展示了在平面波基下电子结构哈密顿量的第一量子化基态能量估计中的渐近门复杂度改进。这种改进依赖于识别哈密顿量的平方和表示，它提供了一个下界证书和低成本块编码，从而导致可证明更低的量子相位估计门成本。通过使用由总电荷密度算符生成的平方和算符来实现，与先前工作相比，块编码归一化改进为$\lambda = \mathcal{O}\left(\eta\Delta^{-1.5}+\eta^{1.5}\Delta^{-1} \right)$ ，而先前工作为$\lambda = \mathcal{O}(\eta\Delta^{-2}+\eta^2\Delta^{-1})$（其中$\eta$是电子数，$\Delta$是模拟网格间距）。证明了块编码归一化和类似块编码成本的渐近降低将材料和化学系统的资源估计减少了$2 - 44\times$，对应于从头算材料模拟的最低成本估计。
英文摘要
We demonstrate an asymptotic gate complexity improvement in first-quantized ground-state energy estimation of electronic structure Hamiltonians in a plane wave basis by employing the sum-of-squares spectral gap amplification protocol. The improvement relies on identifying a sum-of-squares representation of the Hamiltonian which provides a lower bound certificate and low cost block encoding that leads to a provably lower quantum phase estimation gate cost. This is achieved by using a sum-of-squares operator generated by the total charge density operator resulting in a block encoding normalization improvement of $λ= \mathcal{O}\left(ηΔ^{-1.5}+η^{1.5}Δ^{-1} \right)$ compared to prior work $λ= \mathcal{O}(ηΔ^{-2}+η^2Δ^{-1})$ where $η$ is the number of electrons and $Δ$ is the simulation grid spacing. The asymptotic reduction in block encoding normalization and similar block encoding costs to prior work is demonstrated to reduce resource estimates for materials and chemical systems by a factor of $2 - 44\times$ corresponding to the lowest cost estimates for ab initio materials simulation.
