{"paper":{"title":"Nonlinear Quantum Search Using the Gross-Pitaevskii Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"David A. Meyer, Thomas G. Wong","submitted_at":"2013-03-02T10:24:52Z","abstract_excerpt":"We solve the unstructured search problem in constant time by computing with a physically motivated nonlinearity of the Gross-Pitaevskii type. This speedup comes, however, at the novel expense of increasing the time-measurement precision. Jointly optimizing these resource requirements results in an overall scaling of $N^{1/4}$. This is a significant, but not unreasonable, improvement over the $N^{1/2}$ scaling of Grover's algorithm. Since the Gross-Pitaevskii equation approximates the multi-particle (linear) Schr\\\"odinger equation, for which Grover's algorithm is optimal, our result leads to a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0371","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}