{"paper":{"title":"Unitary RQL Equals RQL","arxiv_id":"2610.06231","primary_cat":"quant-ph","submitted_at":"2026-10-05T12:35:05+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. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"Intermediate measurements let quantum computations discard information and reuse their workspace.","hedge":{"p":0.93,"label":"asserted"},"own_p":0.05,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.04,"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":0.97,"id":"s1","own":false,"role":"background","text":"Deferring all measurements can require storing their entire history, which need not preserve logarithmic space.","hedge":{"p":0.54,"label":"asserted"},"own_p":0.09,"main_claim_p":0.02,"quantitative":true,"quantitative_p":0.63,"role_probabilities":{"gap":0.03,"method":0.0,"result":0.0,"background":0.97,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.71,"id":"s2","own":false,"role":"gap","text":"Fefferman and Remscrim proved that measurements can nevertheless be eliminated with two-sided bounded error, and asked whether the same holds with one-sided error [FR21].","hedge":{"p":0.96,"label":"asserted"},"own_p":0.03,"main_claim_p":0.03,"quantitative":true,"quantitative_p":0.75,"role_probabilities":{"gap":0.71,"method":0.0,"result":0.0,"background":0.29,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":3,"p":0.82,"id":"s3","own":true,"role":"result","text":"We prove RQL{\\Gamma} = RQUL{\\Gamma} for the standard gate set {\\Gamma} = {H, T, CNOT}, preserving polynomial time, logarithmic space, and exactly zero acceptance on no-instances.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.97,"main_claim_p":0.93,"quantitative":true,"quantitative_p":0.88,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.82,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.18,"interpretation":0.0}},{"i":4,"p":0.9,"id":"s4","own":true,"role":"method","text":"Our proof extends the density-matrix doubling method of Girish, Raz and Zhan [ GRZ21 ] to general channels, including resets and classical memory.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.9,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.1,"role_probabilities":{"gap":0.0,"method":0.9,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.1,"interpretation":0.0}},{"i":5,"p":0.6,"id":"s5","own":true,"role":"result","text":"We also prove measurement elimination for broader finite gate sets with exact inverses, including suitable gates with transcendental entries, and establish gate-set independence for a specified family of algebraic gate sets.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.13,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.6,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.4,"interpretation":0.0}},{"i":6,"p":0.72,"id":"s6","own":true,"role":"result","text":"A separate history-checking construction proves QMAL1,G = QUMAL1,G under explicit gate assumptions: measurements can also be eliminated from logarithmic-space quantum verification while preserving perfect completeness","hedge":{"p":1.0,"label":"asserted"},"own_p":0.91,"main_claim_p":0.08,"quantitative":true,"quantitative_p":0.79,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.72,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.28,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":1.0,"text":"We prove RQL{\\Gamma} = RQUL{\\Gamma} for the standard gate set {\\Gamma} = {H, T, CNOT}, preserving 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