{"paper":{"title":"Qudit versions of the qubit \"pi-over-eight\" gate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jiri Vala, Mark Howard","submitted_at":"2012-06-07T20:01:13Z","abstract_excerpt":"When visualised as an operation on the Bloch sphere, the qubit \"pi-over-eight\" gate corresponds to one-eighth of a complete rotation about the vertical axis. This simple gate often plays an important role in quantum information theory, typically in situations for which Pauli and Clifford gates are insufficient. Most notably, when it supplements the set of Clifford gates then universal quantum computation can be achieved. The \"pi-over-eight\" gate is the simplest example of an operation from the third level of the Clifford hierarchy (i.e., it maps Pauli operations to Clifford operations under co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1598","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"}