Exact Coset Sampling for Quantum Lattice Algorithms
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.
68c9fc8a6e0073c09bd1ddc2
Yifan Zhang
claimed_verified
2025-09-17T12:57:20.391Z
647bf082aba7062fe5c51ca9
https://cdn-avatars.huggingface.co/v1/production/uploads/647bf082aba7062fe5c51ca9/p4lY9IjHiWZETKmFq1mtU.jpeg
Yifan Zhang
user
yifAI
Exact Coset Sampling for Quantum Lattice Algorithms
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.
A replacement for the domain-extension step in a quantum lattice algorithm uses a pair-shift difference construction to correct periodicity issues and enforce modular linear relations efficiently.
domain-extension windowed-QFT complex-Gaussian windows periodicity/support mismatch pair-shift difference CRT-coset state QFT modular linear relation unitary gates asymptotics