{"paper":{"title":"Fault Tolerant Quantum Computation with Constant Error","arxiv_id":"quant-ph/9611025","primary_cat":"quant-ph","submitted_at":"1996-11-14T11:44:10+00:00","version_compiled":"v2"},"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. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v2","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.03,"main_claim_p":0.03,"quantitative":true,"quantitative_p":0.78,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":0.9,"id":"s1","own":true,"role":"contribution","text":"We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than some constant threshold.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.85,"quantitative":true,"quantitative_p":0.87,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.1,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.9,"interpretation":0.0}},{"i":2,"p":0.94,"id":"s2","own":true,"role":"result","text":"The cost is polylogarithmic in time and space, and no measurements are used during the quantum computation.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.89,"main_claim_p":0.21,"quantitative":false,"quantitative_p":0.28,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.94,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.06,"interpretation":0.0}},{"i":3,"p":0.96,"id":"s3","own":true,"role":"result","text":"The result holds also for quantum circuits which operate on nearest neighbors only.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.82,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.1,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.96,"background":0.0,"limitation":0.01,"future_work":0.0,"contribution":0.03,"interpretation":0.0}},{"i":4,"p":1.0,"id":"s4","own":true,"role":"method","text":"To achieve this noise resistance, we use concatenated quantum error correcting codes.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.87,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":1.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":5,"p":0.47,"id":"s5","own":true,"role":"contribution","text":"The scheme presented is general, and works with all quantum codes that satisfy some restrictions, namely that the code is ``proper''.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.82,"main_claim_p":0.16,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.15,"result":0.11,"background":0.0,"limitation":0.27,"future_work":0.0,"contribution":0.47,"interpretation":0.0}},{"i":6,"p":0.98,"id":"s6","own":true,"role":"contribution","text":"We present two explicit classes of proper quantum codes.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.29,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.98,"interpretation":0.0}},{"i":7,"p":0.89,"id":"s7","own":true,"role":"contribution","text":"The first example of proper quantum codes generalizes classical secret sharing with polynomials.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.79,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.09,"role_probabilities":{"gap":0.0,"method":0.1,"result":0.01,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.89,"interpretation":0.0}},{"i":8,"p":0.74,"id":"s8","own":true,"role":"contribution","text":"The second uses a known class of quantum codes and converts it to a proper code.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.82,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.25,"result":0.01,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.74,"interpretation":0.0}},{"i":9,"p":0.46,"id":"s9","own":false,"role":"method","text":"This class is defined over a field with p elements, so the elementary quantum particle is not a qubit but a ``qupit''.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.44,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.29,"role_probabilities":{"gap":0.0,"method":0.46,"result":0.02,"background":0.03,"limitation":0.14,"future_work":0.0,"contribution":0.34,"interpretation":0.01}},{"i":10,"p":1.0,"id":"s10","own":true,"role":"result","text":"With our codes, the threshold is about 10^(-6).","hedge":{"p":0.92,"label":"asserted"},"own_p":0.9,"main_claim_p":0.16,"quantitative":true,"quantitative_p":0.99,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":11,"p":0.99,"id":"s11","own":false,"role":"future_work","text":"Hopefully, this paper motivates a search for proper quantum codes with higher thresholds, at which point quantum computation becomes 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