{"id":"W3014422752","doi":"10.1080/03081087.2020.1748852","title":"Higher rank matricial ranges and hybrid quantum error correction","year":2020,"lang":"en","type":"article","venue":"Linear and Multilinear Algebra","topic":"Quantum Computing Algorithms and Architecture","field":"Computer Science","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo; University of Guelph","funders":"University of Waterloo; Mitacs; Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada; African Institute for Mathematical Sciences; Simons Foundation","keywords":"Hilbert space; Mathematics; Quantum; Quantum channel; Quantum error correction; Error detection and correction; Rank (graph theory); Dimension (graph theory); Operator (biology); SIC-POVM; Range (aeronautics); Pure mathematics; Discrete mathematics; Algorithm; Quantum information; Quantum operation; Quantum mechanics; Combinatorics; 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":[0.001319561,0.0004797001,0.0005353395,0.001061986,0.0007862614,0.00180971,0.0009182517,0.0007342453,0.003474227],"category_scores_gemma":[0.0055059,0.0002480082,0.0004837333,0.0007446848,0.002795595,0.003899932,0.002429329,0.00186324,0.0007109881],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005202697,"about_ca_system_score_gemma":0.0004448551,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003310766,"about_ca_topic_score_gemma":0.0002336579,"domain_scores_codex":[0.9983871,0.0004011729,0.00007724558,0.0002950332,0.0005620516,0.0002774765],"domain_scores_gemma":[0.9944249,0.002791163,0.0007163936,0.0008559615,0.000869019,0.0003425144],"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":[0.00003093594,0.00001682378,0.0003170152,0.00003520866,0.000008357194,0.00008129024,0.0001336491,0.006583914,0.002370919,0.9838871,0.0004195112,0.006115234],"study_design_scores_gemma":[0.000008969942,0.00006511595,0.0002917432,0.00001721896,0.000006589843,0.0001957272,0.00007702777,0.05824338,0.003669203,0.9347966,0.002594854,0.00003364288],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2110417,0.001189344,0.7493567,0.0008575747,0.000106979,0.00005918375,0.0002853225,0.0003950312,0.03670816],"genre_scores_gemma":[0.9382842,0.0003856003,0.05562591,0.0002140625,0.0001652365,0.00007865658,0.0001579645,0.00006411735,0.005024256],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003474227,"threshold_uncertainty_score":0.01162249,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01693686277610948,"score_gpt":0.2472565448273012,"score_spread":0.2303196820511917,"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."}}