{"paper":{"title":"Complex Hadamard Matrices, Instantaneous Uniform Mixing and Cubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ada Chan","submitted_at":"2013-05-24T17:44:44Z","abstract_excerpt":"We study the continuous-time quantum walks on graphs in the adjacency algebra of the $n$-cube and its related distance regular graphs.\n  For $k\\geq 2$, we find graphs in the adjacency algebra of $(2^{k+2}-8)$-cube that admit instantaneous uniform mixing at time $\\pi/2^k$ and graphs that have perfect state transfer at time $\\pi/2^k$.\n  We characterize the folded $n$-cubes, the halved $n$-cubes and the folded halved $n$-cubes whose adjacency algebra contains a complex Hadamard matrix. We obtain the same conditions for the characterization of these graphs admitting instantaneous uniform mixing."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5811","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"}