{"schema_version":"0.1","map_id":"paper-60-map","publication_id":60,"publication_anchor":"paper-60","slug":"paper-60","canonical_path":"/knowledge/papers/paper-60/","machine_path":"/knowledge/papers/paper-60.json","root_node_id":"paper-60","stage":"mapped_draft","contribution_type_vocabulary_version":"0.1","contribution_types":["algorithm"],"title":"Quantum Optimization Heuristics with an Application to Knapsack Problems","year":2021,"status":"Published","venue":"IEEE International Conference on Quantum Computing and Engineering (QCE)","topic":"algorithms-foundations","labels":["Theory","Applied"],"authors":["Wim van Dam","Karim Eldefrawy","Nicholas Genise","Natalie Parham"],"keywords":["quantum optimization","QAOA","knapsack","constrained optimization"],"research_question":"Can shallow QAOA-style heuristics use a classical greedy solution to stay near feasible high-value regions of a constrained knapsack search space and outperform comparably simple classical heuristics?","central_answer":"The paper initializes qubits from smoothed greedy marginals and introduces hourglass and copula mixers that preserve those biases while exploring nearby solutions. Statevector simulations on small hard-instance families report better performance than selected shallow classical baselines, with explicit classical-simulability and scaling caveats.","curation":{"drafted_at":"2026-07-11","drafted_by":[{"actor_type":"ai","name":"OpenAI Codex","role":"full-text extraction, algorithm-and-experiment mapping, and initial assessment"}],"method":"Complete review of the 21-page arXiv manuscript, including derivations, pseudocode, hard-instance generators, parameter optimization, comparisons, conclusions, and visual inspection of title and simulation-result pages. Claims are bounded to depth-one statevector simulations at n equals 10 and the selected baselines.","source_scope":"full_source_audit","approval":{"status":"pending","note":"AI-authored source map awaiting full author verification. Mixer descriptions, experimental settings, and interpretation of comparative results should be checked."}},"sources":[{"id":"source-paper-60-archive-pdf","type":"public_archive_copy","title":"Quantum Optimization Heuristics with an Application to Knapsack Problems","url":"/pubs/2021/quantum-optimization-knapsack.pdf","provenance_category":"archive","retrieved_from":"https://arxiv.org/pdf/2108.08805","media_type":"application/pdf","sha256":"d403fa39c25c7b77b806b19cc86dee9c1a2dab74976f6d9fdb967230d5603ac5","page_count":21},{"id":"source-paper-60-official","type":"official_publication_record","title":"IEEE QCE 2021 publication record","url":"https://doi.org/10.1109/QCE52317.2021.00033","provenance_category":"official"},{"id":"source-paper-60-citations","type":"citation_index_snapshot","title":"OpenAlex work 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constant-depth initial state near the capacity boundary rather than a uniform superposition.","source_anchor_ids":["anchor-paper-60-mixers","anchor-paper-60-qkp"]},{"id":"paper-60-method-hourglass","kind":"algorithm","parent_id":"paper-60-method","order":1,"epistemic_status":"specified","title":"QKP hourglass mixer","summary":"A single-qubit mixer has each biased marginal state as an eigenstate, preserving the chosen product-distribution bias while the objective phase steers probability toward higher-value strings.","source_anchor_ids":["anchor-paper-60-mixers","anchor-paper-60-qkp"]},{"id":"paper-60-method-copula","kind":"algorithm","parent_id":"paper-60-method","order":2,"epistemic_status":"specified","title":"QKP copula mixer","summary":"Two-qubit copula operations preserve individual marginals while adding tunable correlations; the evaluated ring construction favors anticorrelation so neighboring items are less likely to be jointly selected.","source_anchor_ids":["anchor-paper-60-mixers","anchor-paper-60-qkp"]},{"id":"paper-60-baselines","kind":"evidence_group","parent_id":"paper-60","order":5,"epistemic_status":"controlled_simulation","title":"Comparison design","summary":"Quantum heuristics are compared with lazy greedy, very greedy, warm-start simulated annealing, and a global one-step annealing variant on strongly correlated, inverse-strong, profit, and two spanner distributions.","source_anchor_ids":["anchor-paper-60-instances","anchor-paper-60-classical"]},{"id":"paper-60-parameters","kind":"method","parent_id":"paper-60-baselines","order":1,"epistemic_status":"per_instance_optimized","title":"Parameter search","summary":"Quantum angles are grid-searched then refined with BFGS for each instance across bias strengths and selected copula correlations; simulated annealing temperature is also tuned per instance from repeated trials.","source_anchor_ids":["anchor-paper-60-classical","anchor-paper-60-quantum"]},{"id":"paper-60-claim-comparison","kind":"claim","parent_id":"paper-60","order":6,"epistemic_status":"simulation_result","title":"Better results than selected shallow heuristics","summary":"Across the sampled ten-item instances, the hourglass variant typically exceeds the four chosen classical heuristics and the copula variant improves further; infeasible outputs count as zero rather than being postselected away.","source_anchor_ids":["anchor-paper-60-results"]},{"id":"paper-60-claim-sensitivity","kind":"claim","parent_id":"paper-60","order":7,"epistemic_status":"numerical_observation","title":"Limited sensitivity on the tested size","summary":"The tested copula mixer generally prefers maximal anticorrelation, performance varies weakly across the sampled bias strengths, and favorable beta angles cluster in two regions, suggesting some parameter reuse at n equals 10.","source_anchor_ids":["anchor-paper-60-results"]},{"id":"paper-60-boundaries","kind":"limitation_group","parent_id":"paper-60","order":8,"epistemic_status":"material","title":"Boundaries","summary":"Experiments are statevector simulations at n equals 10 and depth one, use heavily optimized per-instance parameters, and compare only simple classical methods. The authors expect more elaborate classical algorithms to outperform these quantum heuristics and leave larger n, deeper p, and parameter-scaling behavior open.","source_anchor_ids":["anchor-paper-60-quantum","anchor-paper-60-results","anchor-paper-60-conclusion"]},{"id":"paper-60-boundary-classical","kind":"limitation","parent_id":"paper-60-boundaries","order":1,"epistemic_status":"explicitly_acknowledged","title":"Hourglass path can be quantum-inspired classical","summary":"For a linear objective such as knapsack, the first non-entangling technique can be classically simulated with comparable circuit complexity, so its improvement is not evidence of quantum advantage.","source_anchor_ids":["anchor-paper-60-problem","anchor-paper-60-conclusion"]},{"id":"paper-60-evidence","kind":"evidence_group","parent_id":"paper-60","order":9,"epistemic_status":"analytical_and_simulated","title":"Evidence boundary","summary":"The paper supplies circuit derivations, pseudocode, instance generators, baseline settings, scatter plots, and sensitivity results. It supplies neither hardware experiments nor a proof of asymptotic advantage.","source_anchor_ids":["anchor-paper-60-mixers","anchor-paper-60-instances","anchor-paper-60-results"]},{"id":"paper-60-resources","kind":"artifact_group","parent_id":"paper-60","order":10,"epistemic_status":"source_available","title":"Publication resources","summary":"The checked-in arXiv manuscript has fixity metadata and the DOI identifies the IEEE publication. No code or data artifact is represented in the paper map.","source_anchor_ids":["anchor-paper-60-problem","anchor-paper-60-publication"]},{"id":"paper-60-scrutiny","kind":"scrutiny","parent_id":"paper-60","order":11,"epistemic_status":"venue_reviewed","title":"External scrutiny","summary":"The paper appeared at IEEE QCE 2021. 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