{"paper":{"title":"Universal quantum computation in a hidden basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Lawrence M. Ioannou, Michele Mosca","submitted_at":"2008-10-15T19:31:58Z","abstract_excerpt":"Let $\\ket{\\0}$ and $\\ket{\\1}$ be two states that are promised to come from known subsets of orthogonal subspaces, but are otherwise unknown. Our paper probes the question of what can be achieved with respect to the basis $\\{\\ket{\\0},\\ket{\\1}}^{\\otimes n}$ of $n$ logical qubits, given only a few copies of the unknown states $\\ket{\\0}$ and $\\ket{\\1}$. A phase-invariant operator is one that is unchanged under the relative phase-shift $\\ket{\\1} \\mapsto e^{i \\theta}\\ket{\\1}$, for any $\\theta$, of all of the $n$ qubits. We show that phase-invariant unitary operators can be implemented exactly with n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.2780","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"}