{"paper":{"title":"Quantum algorithms for path and cycle containment problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A dichotomy for path-containment problems shows some are solvable with linear queries while others are equivalent to cycle problems and admit a quantum-walk algorithm with query complexity Õ(n^{3/2 - α_k}) where α_k decays exponentially in k, plus a conditional lower bound.","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Amin Shiraz Gilani, Arjan Cornelissen, Subhasree Patro","submitted_at":"2026-05-09T15:55:07Z","abstract_excerpt":"The quantum query complexity of subgraph-containment problems, which ask whether a given subgraph $H$ is present in an input graph $G$, has been the subject of considerable study. However, even for relatively simple subgraphs, such as paths and cycles, a complete understanding of their query complexities remains elusive. In this work, we consider several variants of path- and cycle-containment problems in the adjacency matrix model, where we search for paths or cycles of constant length $k$. We compare the settings where the graphs are directed or undirected, where the goal is to detect or fin"},"claims":{"count":3,"items":[{"kind":"strongest_claim","text":"We prove a novel quantum-walk-based algorithm that achieves query complexity Õ(n^{3/2-α_k}), where α_k ∈ Θ(c^{-k}) and c = √(3+√17)/2 ≈ 1.33, beating the previous best upper bound O(n^{3/2}).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The randomized reductions between problem variants preserve quantum query complexity up to constant factors; if this fails for any of the listed variants, the claimed equivalence classes and the transfer of the new upper bound would collapse.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A dichotomy for path-containment problems shows some are solvable with linear queries while others are equivalent to cycle problems and admit a quantum-walk algorithm with query complexity Õ(n^{3/2 - α_k}) where α_k decays exponentially in k, plus a conditional lower bound.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"}],"snapshot_sha256":"85ce52c271ee2fbb55b6204e8631182dbe14edb1c58a67ca60580d7cb7326f42"},"source":{"id":"2605.09017","kind":"arxiv","version":2},"verdict":{"id":"2dcd2cf8-f17a-48c1-89dc-7dbc7f1e6d27","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T02:15:46.902250Z","strongest_claim":"We prove a novel quantum-walk-based algorithm that achieves query complexity Õ(n^{3/2-α_k}), where α_k ∈ Θ(c^{-k}) and c = √(3+√17)/2 ≈ 1.33, beating the previous best upper bound O(n^{3/2}).","one_line_summary":"A dichotomy for path-containment problems shows some are solvable with linear queries while others are equivalent to cycle problems and admit a quantum-walk algorithm with query complexity Õ(n^{3/2 - α_k}) where α_k decays exponentially in k, plus a conditional lower bound.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The randomized reductions between problem variants preserve quantum query complexity up to constant factors; if this fails for any of the listed variants, the claimed equivalence classes and the transfer of the new upper bound would collapse.","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.09017/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T08:22:01.745028Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T20:39:13.843341Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T14:01:19.108676Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T10:37:35.596257Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"bd1c7eca4c9d13290b0f0a4605d601683b5d6cb2d69f3d6f853e05056b4198f1"},"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"}