{"paper":{"title":"Exact Coset Sampling for Quantum Lattice Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CL","cs.CR"],"primary_cat":"quant-ph","authors_text":"Yifan Zhang","submitted_at":"2025-09-15T18:10:28Z","abstract_excerpt":"We revisit the post-processing phase of Chen's Karst-wave quantum lattice algorithm (Chen, 2024) in the Learning with Errors (LWE) parameter regime. Conditioned on a transcript $E$, the post-Step 7 coordinate state on $(\\mathbb{Z}_M)^n$ is supported on an affine grid line $\\{\\, j\\Delta + v^{\\ast}(E) + M_2 k \\bmod M : j \\in \\mathbb{Z},\\ k \\in \\mathcal{K} \\,\\}$, with $\\Delta = 2D^2 b$, $M = 2M_2 = 2D^2 Q$, and $Q$ odd. The amplitudes include a quadratic Karst-wave chirp $\\exp(-2\\pi i j^2 / Q)$ and an unknown run-dependent offset $v^{\\ast}(E)$. We show that Chen's Steps 8-9 can be replaced by a s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.12341","kind":"arxiv","version":8},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}