{"paper":{"title":"Concatenated Quantum Codes","arxiv_id":"quant-ph/9608012","primary_cat":"quant-ph","submitted_at":"1996-08-08T23:13:46+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. 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error.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.04,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.31,"role_probabilities":{"gap":0.19,"method":0.0,"result":0.0,"background":0.81,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.55,"id":"s2","own":true,"role":"contribution","text":"In this report a method is given which has the property that to store or transmit a qubit with maximum error $\\epsilon$ requires gates with error at most $c\\epsilon$ and storage or channel elements with error at most $\\epsilon$, independent of how long we wish to store the state or how far we wish to transmit it.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.9,"main_claim_p":0.89,"quantitative":true,"quantitative_p":0.94,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.45,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.55,"interpretation":0.0}},{"i":3,"p":0.98,"id":"s3","own":true,"role":"method","text":"The method relies on using concatenated quantum codes with hierarchically implemented recovery operations.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.71,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.98,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.02,"interpretation":0.0}},{"i":4,"p":0.96,"id":"s4","own":true,"role":"result","text":"The overhead of the method is polynomial in the time of storage or the distance of the transmission.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.85,"main_claim_p":0.08,"quantitative":true,"quantitative_p":0.66,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.96,"background":0.0,"limitation":0.02,"future_work":0.0,"contribution":0.02,"interpretation":0.0}},{"i":5,"p":0.62,"id":"s5","own":true,"role":"result","text":"Rigorous and heuristic lower bounds for the constant $c$ are 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