Exact Coset Sampling for Quantum Lattice Algorithms

Yifan Zhang

Exact Coset Sampling for Quantum Lattice Algorithms: 2 upvotes on Hugging Face Daily Papers, #15 of 21 papers on 2025-09-17. Day-by-day upvote history.

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.

Paper page on Hugging Face · arXiv

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