{"paper":{"title":"Quantum Riemannian Hamiltonian Descent","arxiv_id":"2603.28624","primary_cat":"quant-ph","submitted_at":"2026-03-30T16:08:26+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. 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quantum corrections appear in the action integral but they are suppressed at late times by the time-dependent dissipation factor.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.13,"quantitative":false,"quantitative_p":0.29,"role_probabilities":{"gap":0.0,"method":0.43,"result":0.27,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.3,"interpretation":0.0}},{"i":2,"p":1.0,"id":"s2","own":true,"role":"interpretation","text":"This implies that convergence near optimal points is controlled by the classical potential while quantum effects influence early-time dynamics.","hedge":{"p":0.9,"label":"asserted"},"own_p":0.8,"main_claim_p":0.35,"quantitative":false,"quantitative_p":0.24,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":1.0}},{"i":3,"p":0.62,"id":"s3","own":true,"role":"contribution","text":"By analyzing the semiclassical equation, we estimate a lower bound on the convergence time and numerically demonstrate whether QRHD works as a quantum optimization algorithm in some examples.","hedge":{"p":0.86,"label":"asserted"},"own_p":0.94,"main_claim_p":0.14,"quantitative":true,"quantitative_p":0.71,"role_probabilities":{"gap":0.0,"method":0.27,"result":0.11,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.62,"interpretation":0.0}},{"i":4,"p":0.54,"id":"s4","own":true,"role":"contribution","text":"A quantum circuit implementation based on time-dependent Hamiltonian simulation is also discussed and the query complexity is estimated.","hedge":{"p":0.87,"label":"asserted"},"own_p":0.81,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.46,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.54,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":0.72,"text":"This implies that convergence near optimal points is controlled by the 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