量子晶格算法的精確陪集採樣

摘要

我們提出了一種簡單、完全正確且假設較少的替代方案，用於替換近期帶有複數高斯窗的窗口化量子傅立葉變換（QFT）晶格算法~chen2024quantum中備受爭議的“域擴展”步驟（第9步）。已發表的第9步存在週期性/支撐不匹配的問題。我們提出了一種配對位移差分構造，能夠相干地消除所有未知偏移量，精確生成Z_{P}上的均勻中國剩餘定理（CRT）陪集態，然後利用QFT來強制執行預期的模線性關係。該單元操作是可逆的，使用多項式對數級（poly(log M_2)）的量子門，並保持了算法的漸近性能。項目頁面：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.

量子晶格算法的精確陪集採樣

Exact Coset Sampling for Quantum Lattice Algorithms

摘要

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