{"paper":{"title":"A hybrid quantum-classical lattice kinetic scheme with tensor-train feedback for incompressible flows","arxiv_id":"2611.04500","primary_cat":"math-ph","submitted_at":"2026-11-03T08:26:46+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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size.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.13,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.28,"role_probabilities":{"gap":0.06,"method":0.0,"result":0.0,"background":0.93,"limitation":0.01,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.74,"id":"s2","own":true,"role":"contribution","text":"We construct a tensor-train (TT) interface that retains reusable classical cores at the physical amplitude scale for a full-relaxation lattice kinetic scheme.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.16,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.26,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.74,"interpretation":0.0}},{"i":3,"p":0.98,"id":"s3","own":true,"role":"method","text":"The cores supply nonlinear coefficients and prepare each quantum input.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.75,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.98,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.02,"interpretation":0.0}},{"i":4,"p":1.0,"id":"s4","own":true,"role":"method","text":"Energy-scaled propagation and coordinate recovery encode the updated distribution, and alternating least-squares reconstruction converts signed Hadamard-test overlaps into output cores by restoring a known normalization factor.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.86,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.07,"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":0.96,"id":"s5","own":true,"role":"method","text":"The next step starts from accepted cores without replaying previous quantum evolution.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.6,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.96,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.04,"interpretation":0.0}},{"i":6,"p":0.49,"id":"s6","own":true,"role":"contribution","text":"Under positive, unit-sum reference coefficients, positive lower and finite upper density bounds, and Lipschitz equilibrium sensitivity, perturbation bounds relate local defects to feedback errors.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.72,"main_claim_p":0.06,"quantitative":true,"quantitative_p":0.68,"role_probabilities":{"gap":0.0,"method":0.34,"result":0.14,"background":0.01,"limitation":0.01,"future_work":0.0,"contribution":0.49,"interpretation":0.01}},{"i":7,"p":0.51,"id":"s7","own":true,"role":"method","text":"Resource bounds account for classical operations, circuit execution, sampling, and verification.","hedge":{"p":0.94,"label":"asserted"},"own_p":0.63,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.17,"role_probabilities":{"gap":0.0,"method":0.51,"result":0.04,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.45,"interpretation":0.0}},{"i":8,"p":0.88,"id":"s8","own":true,"role":"result","text":"Classical diagnostics expose why distribution accuracy alone is insufficient: in 80-step feedback on a $16\\times16$ grid, rank cap 4 nearly eliminates the vortex despite a final distribution error below $1\\%$, whereas rank cap 12 gives relative velocity error $1.03\\times10^{-3}$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.92,"main_claim_p":0.19,"quantitative":true,"quantitative_p":0.99,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.88,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.12}},{"i":9,"p":0.98,"id":"s9","own":true,"role":"result","text":"Four-step binomial readout simulations show that tightening core sampling tolerance threefold raises the prescribed sufficient budget from $5.97\\times10^{12}$ to $5.37\\times10^{13}$ shots as the result approaches the fixed-rank, fixed-sweep exact-overlap trajectory.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.88,"main_claim_p":0.07,"quantitative":true,"quantitative_p":0.99,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.98,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":10,"p":0.82,"id":"s10","own":true,"role":"interpretation","text":"The interface therefore provides a way to connect quantum propagation to nonlinear feedback and to assess the separate demands of compression, velocity accuracy, and readout 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