{"paper":{"title":"Perfect state transfer in cubelike graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.CO","authors_text":"Chris Godsil, Wang-Chi Cheung","submitted_at":"2010-10-22T14:22:52Z","abstract_excerpt":"Suppose $C$ is a subset of non-zero vectors from the vector space $\\mathbb{Z}_2^d$. The cubelike graph $X(C)$ has $\\mathbb{Z}_2^d$ as its vertex set, and two elements of $\\mathbb{Z}_2^d$ are adjacent if their difference is in $C$. If $M$ is the $d\\times |C|$ matrix with the elements of $C$ as its columns, we call the row space of $M$ the code of $X$. We use this code to study perfect state transfer on cubelike graphs. Bernasconi et al have shown that perfect state transfer occurs on $X(C)$ at time $\\pi/2$ if and only if the sum of the elements of $C$ is not zero. Here we consider what happens "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4721","kind":"arxiv","version":2},"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"}