发表机构
University of Waterloo; Perimeter Institute for Theoretical Physics; Microsoft Quantum; Massachusetts Institute of Technology; University of California, Santa Barbara; National Research Council Canada（滑铁卢大学; 理论物理前沿研究所; 微软量子; 麻省理工学院; 加州大学圣塔芭芭拉分校; 加拿大国家研究委员会）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究关联实值周期函数光滑度与量子态制备成本，利用Gevrey正则性提出高效量子PDE求解傅里叶方法，可转化为门计数，还构建多体量子模拟流水线获多项式级量子加速。
AI 中文摘要
我们将实值周期函数的不同光滑度与其高精度傅里叶基振幅编码制备为量子态的成本相关联。核心发现是，对光滑函数与解析函数之间的空间进行分层的Gevrey层级，为高精度量子算法提供了一类自然的函数空间。随后，我们专门研究求解一般线性偏微分方程（PDE），展示了我们的傅里叶方法如何在量子计算机上以不同的目标精度高效求解此类方程。这也证明了我们的框架能够将查询复杂度结果转化为明确的基本门计数。作为应用，我们引入了多体量子模拟流水线的层级结构，该结构利用这些高精度算法在第一性原理量化中探究原子系统的线性响应。该层级的每一级都能解锁更高次多项式级别的量子加速，随着量子计算机的规模化，模拟效率将逐步提升。
英文摘要
We connect different degrees of smoothness of real-valued periodic functions to the number of qubits required for their high-precision Fourier-basis amplitude encodings. Our central observation is that the Gevrey hierarchy, which stratifies the space between smooth and analytic functions, provides a natural class for high-precision quantum algorithms. We use Gevrey regularity to analyze a quantum algorithm for solving general linear partial differential equations (PDEs) with periodic boundary conditions. We then extend the solver to PDEs with Dirichlet boundary conditions using thin Gevrey collars and a regularized inverse. Our resource bounds specify precision-dependent Fourier cutoffs and account for restricted discrete stability, elementary gate costs, and restriction to the Dirichlet domain. Finally, we apply our approach to isotropic and anisotropic Poisson equations with periodic and Dirichlet boundary conditions.
