Exact Coset Sampling for Quantum Lattice Algorithms
Authors: name: Yifan Zhang

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.