{"paper":{"title":"Reply to Andrew Hodges","arxiv_id":"quant-ph/0602214","primary_cat":"quant-ph","submitted_at":"2006-02-26T12:08:19+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":0.5,"id":"s0","own":true,"role":"method","text":"We separate the criticisms of Hodges \\cite{Hodges2005} and others into those against the algorithm itself and those against its physical implementation.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.77,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.14,"role_probabilities":{"gap":0.0,"method":0.5,"result":0.0,"background":0.05,"limitation":0.0,"future_work":0.0,"contribution":0.45,"interpretation":0.0}},{"i":1,"p":0.47,"id":"s1","own":true,"role":"contribution","text":"We then point out that {\\em all} those against the algorithm are either misleading or misunderstanding, and that the algorithm is self consistent.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.86,"main_claim_p":0.36,"quantitative":false,"quantitative_p":0.28,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.47,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.47,"interpretation":0.04}},{"i":2,"p":0.36,"id":"s2","own":false,"role":"result","text":"The only central argument against physical implementations of the algorithm, on the other hand, is based on an assumption that its Hamiltonians cannot be effectively constructed due to a lack of infinite precision.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.21,"main_claim_p":0.15,"quantitative":false,"quantitative_p":0.3,"role_probabilities":{"gap":0.03,"method":0.01,"result":0.36,"background":0.27,"limitation":0.03,"future_work":0.0,"contribution":0.21,"interpretation":0.09}},{"i":3,"p":0.48,"id":"s3","own":false,"role":"gap","text":"However, so far there is no known physical principle dictating why that cannot be done.","hedge":{"p":0.96,"label":"asserted"},"own_p":0.13,"main_claim_p":0.14,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.48,"method":0.0,"result":0.12,"background":0.19,"limitation":0.0,"future_work":0.0,"contribution":0.04,"interpretation":0.17}},{"i":4,"p":0.51,"id":"s4","own":false,"role":"contribution","text":"To show that the criticism may not be a forgone conclusion, we point out the virtually unknown fact that, on the contrary, simple instances of Diophantine equations with apparently {\\em infinitely precisely} integer coefficients have {\\em already} been realised in experiments for certain quantum phase transitions.","hedge":{"p":0.92,"label":"asserted"},"own_p":0.18,"main_claim_p":0.17,"quantitative":false,"quantitative_p":0.15,"role_probabilities":{"gap":0.06,"method":0.01,"result":0.4,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.51,"interpretation":0.02}},{"i":5,"p":0.78,"id":"s5","own":false,"role":"future_work","text":"We also speculate on how central limit theorem of statistics might be of some help in the effective implementation of the required Hamiltonians.","hedge":{"p":1.0,"label":"speculative"},"own_p":0.18,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.03,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.78,"contribution":0.17,"interpretation":0.02}}]},"compiled":{"main_claim":{"p":0.51,"text":"However, so far there is no known physical principle dictating why that cannot be done.","location":"abstract 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