{"id":"W2192515608","doi":"10.1103/physreva.96.062336","title":"Multiqubit Clifford groups are unitary 3-designs","year":2017,"lang":"en","type":"article","venue":"Physical review. A/Physical review, A","topic":"Quantum Computing Algorithms and Architecture","field":"Computer Science","cited_by":189,"is_retracted":false,"has_abstract":true,"ca_institutions":"Perimeter Institute","funders":"Deutsche Forschungsgemeinschaft; Government of Canada","keywords":"Unitary group; Unitary state; Clifford algebra; Dimension (graph theory); Pure mathematics; Mathematics; Group (periodic table); Algebra over a field; Special unitary group; Quantum computer; Quantum; Quantum mechanics; Physics; Mathematical physics","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001012804,0.0004666022,0.0004709052,0.0009228464,0.001237153,0.002312014,0.0005089284,0.001091693,0.006245368],"category_scores_gemma":[0.002475641,0.0003726352,0.0008095175,0.0006287514,0.003945693,0.002704368,0.001474236,0.001244954,0.001089481],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006034914,"about_ca_system_score_gemma":0.000809985,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000196977,"about_ca_topic_score_gemma":0.0001796873,"domain_scores_codex":[0.9988439,0.0003428004,0.00008969935,0.0002450337,0.0002479628,0.0002306617],"domain_scores_gemma":[0.9982975,0.0004591903,0.0003676015,0.0004944318,0.0002229625,0.0001581992],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00005821148,0.00001437035,0.0001727782,0.00005464714,0.000007657226,0.00004599605,0.0001190655,0.001125117,0.00312696,0.9813915,0.0005291496,0.01335451],"study_design_scores_gemma":[0.00003311195,0.0001870134,0.0002542264,0.00004320482,0.00001064941,0.0002227712,0.00008806927,0.007335376,0.008089208,0.9691965,0.01450345,0.00003641911],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3848473,0.002114955,0.517942,0.001327701,0.0006213184,0.0002584098,0.0003374231,0.0006369405,0.09191406],"genre_scores_gemma":[0.8994244,0.0008838277,0.08660459,0.00064987,0.0002178431,0.0003653114,0.0001713069,0.0001824128,0.01150031],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006245368,"threshold_uncertainty_score":0.02089286,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03343235252658291,"score_gpt":0.3680474721133176,"score_spread":0.3346151195867347,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}