{"paper":{"title":"On the class of diffusion operators for fast quantum search","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Avatar Tulsi","submitted_at":"2016-10-18T15:01:01Z","abstract_excerpt":"Grover's quantum search algorithm evolves a quantum system from a known source state $|s\\rangle$ to an unknown target state $|t\\rangle$ using the selective phase inversions, $I_{s}$ and $I_{t}$, of these two states. In one of the generalizations of Grover's algorithm, $I_{s}$ is replaced by a general diffusion operator $D_{s}$ having $|s\\rangle$ as an eigenstate and $I_{t}$ is replaced by a general selective phase rotation $I_{t}^{\\phi}$. A fast quantum search is possible as long as the operator $D_{s}$ and the angle $\\phi$ satisfies certain conditions. These conditions are very restrictive in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05661","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":""},"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"}