{"paper":{"title":"A quantum algorithm for solving 0-1 Knapsack problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"quant-ph","authors_text":"Andreea-Iulia Lefterovici, Lennart Binkowski, Michael Perk, S\\'andor Fekete, S\\\"oren Wilkening, Tobias J. Osborne","submitted_at":"2023-10-10T13:40:30Z","abstract_excerpt":"Here we present two novel contributions for achieving quantum advantage in solving difficult optimisation problems, both in theory and foreseeable practice. (1) We introduce the \"Quantum Tree Generator\", an approach to generate in superposition all feasible solutions of a given instance, yielding together with amplitude amplification the optimal solutions for 0-1 knapsack problems. The QTG offers massive memory savings and enables competitive runtimes compared to the classical state-of-the-art knapsack solvers (such as COMBO, Gurobi, CP-SAT, Greedy) already for instances involving as few as 10"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.06623","kind":"arxiv","version":2},"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/2310.06623/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"}