{"paper":{"title":"An Entropy-Governed Speedup for Quantum Algorithms on Local Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"quant-ph","authors_text":"(2) University of Hyogo, Fran\\c{c}ois Le Gall (1), Japan, Japan), Ranitha Mataraarachchi (1), Suguru Tamaki (2) ((1) Nagoya University","submitted_at":"2026-05-18T11:36:43Z","abstract_excerpt":"Low-energy estimation and state preparation for general $k$-local Hamiltonians are fundamental challenges in quantum complexity theory. For constant relative accuracy, Buhrman et al. (PRL 2025) recently broke the natural Grover bound $O(2^{n/2})$, where $n$ denotes the number of qubits, for both problems. In this paper, for any sufficiently small parameter $d\\ge 0$, we present an even faster quantum algorithm that outputs a quantum state with energy bounded by the minimum energy over all depth-$d$ states (i.e., states obtained by applying a depth-$d$ circuit to the all-zero state), together wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18241","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/2605.18241/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-19T23:41:58.907735Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.279666Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"aa26f02508edc83187e0f7046b6dea4a2d18cfdf674f21da6cffceb86ea92bf8"},"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"}