{"paper":{"title":"Efficient Quantum Algorithm for Mixed-State Quantum Geometry","arxiv_id":"2610.24686","primary_cat":"quant-ph","submitted_at":"2026-10-17T13:38:55+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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computation.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.06,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.41,"role_probabilities":{"gap":0.46,"method":0.0,"result":0.0,"background":0.54,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":1.0,"id":"s2","own":true,"role":"contribution","text":"Here we address the challenge and develop a novel quantum algorithmic framework for efficiently accessing the quantum Fisher information matrix (QFIM) and quantum geometric tensor (QGT) of mixed states.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.16,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":1.0,"interpretation":0.0}},{"i":3,"p":0.8,"id":"s3","own":true,"role":"method","text":"Our key insight is to uncover a previously unexplored connection between the positive semidefinite structure of density matrices and exponentially convergent Gauss-Laguerre quadrature, enabling an efficient integral-based construction of the SLD.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.11,"quantitative":false,"quantitative_p":0.2,"role_probabilities":{"gap":0.0,"method":0.8,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.2,"interpretation":0.0}},{"i":4,"p":0.61,"id":"s4","own":true,"role":"result","text":"A rigorous complexity analysis further establishes the resource efficiency of our algorithm, demonstrating logarithmic precision dependence and double-logarithmic ancillary-qubit overhead at fixed conditioning.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.12,"quantitative":true,"quantitative_p":0.9,"role_probabilities":{"gap":0.0,"method":0.06,"result":0.61,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.33,"interpretation":0.0}},{"i":5,"p":0.73,"id":"s5","own":true,"role":"result","text":"Building on this construction, we achieve near-Heisenberg precision scaling for diagonal QFI estimation without quantum phase estimation and construct unified block encodings of the full QFIM and QGT under a bounded spectral-gap assumption.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.17,"quantitative":true,"quantitative_p":0.87,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.73,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.26,"interpretation":0.0}},{"i":6,"p":0.74,"id":"s6","own":true,"role":"contribution","text":"A complementary regularized algorithm extends efficient diagonal estimation to exponentially small spectral gaps under a bounded-response 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