{"paper":{"title":"Geometry-Informed Polynomial Time Quantum Approximation Schemes for Constrained Optimisation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","cs.DM","math-ph","math.MP","physics.app-ph"],"primary_cat":"quant-ph","authors_text":"Chinonso Onah, Kristel Michielsen","submitted_at":"2026-08-02T09:35:42Z","abstract_excerpt":"When does a noisy quantum sampler yield an end-to-end polynomial-time optimization algorithm with performance guarantees? Building on finite-depth and finite-shot guarantees for Constraint-Enhanced QAOA, we show that inverse-polynomial ideal probability on the optimal set, together with independent sampling, polynomial-time feasibility repair, and scoring, produces an exact-hit fully polynomial randomized approximation scheme, which we call an FPRASq.\n  This guarantee survives device noise within an instance-dependent window. For effective circuit depth linear in the product of layer count and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.01121","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.01121/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}