量子格点算法的精确陪集采样

摘要

我们提出了一种简单、完全正确且假设条件宽松的替代方案，用于替换近期带有复高斯窗的窗口化QFT格点算法~chen2024quantum中备受争议的第9步“域扩展”。已发布的第9步存在周期性与支撑集不匹配的问题。我们引入了一种成对位移差分构造，该构造能够相干地消除所有未知偏移量，精确生成Z_{P}上的均匀CRT陪集态，随后利用QFT强制实施预期的模线性关系。该酉变换是可逆的，仅需多项式对数级（poly(log M_2)）的门操作，并保持了算法的渐近性能。项目页面：https://github.com/yifanzhang-pro/quantum-lattice。

English

We give a simple, fully correct, and assumption-light replacement for the contested "domain-extension" in Step 9 of a recent windowed-QFT lattice algorithm with complex-Gaussian windows~chen2024quantum. The published Step~9 suffers from a periodicity/support mismatch. We present a pair-shift difference construction that coherently cancels all unknown offsets, produces an exact uniform CRT-coset state over Z_{P}, and then uses the QFT to enforce the intended modular linear relation. The unitary is reversible, uses poly(log M_2) gates, and preserves the algorithm's asymptotics. Project Page: https://github.com/yifanzhang-pro/quantum-lattice.

量子格点算法的精确陪集采样

Exact Coset Sampling for Quantum Lattice Algorithms

摘要

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