发表机构
Technion – Israel Institute of Technology; Tel-Hai University of Kiryat Shmona in the Galilee; MIGAL – Galilee Research Institute（以色列理工学院; 加利利基里亚特谢莫纳泰尔海大学; 米加尔加利利研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于自适应采样的高效非均匀量子厄米变换，以近线性逻辑门和对数量子宽度实现精确基变换，并保证算子误差界。
AI 中文摘要
在前$N$个振子模式的张成空间上，高斯-厄米求积给出了模式系数与$N$个加权位置空间样本之间的精确基变换。我们以$O(N\operatorname{polylog}(N,1/\varepsilon))$个逻辑门和对数级量子宽度实现该变换。算子误差界$\varepsilon$对任意叠加态成立，并包含所有辅助寄存器。该构造使用自适应窗口上的符号平均值，将均匀网格样本转换为加权厄米根样本。其变化的宽度控制放大成本，从而得到近线性界。
英文摘要
On the span of the first $N$ oscillator modes, Gauss--Hermite quadrature gives an exact change of basis between mode coefficients and $N$ weighted position space samples. We implement this transform with $O(N\operatorname{polylog}(N,1/\varepsilon))$ logical gates and polylogarithmic quantum width. The operator-error bound $\varepsilon$ holds on arbitrary superpositions and includes all auxiliary registers. The construction uses signed averages on adaptive windows to convert uniform-grid samples into weighted Hermite-root samples. Their varying widths control the amplification cost, giving the near-linear bound.
Comments30 pages, including supplementary material. Minor corrections to notation and exposition; improved figure legibility and ancillary documentation. Results unchanged
