{"paper":{"title":"Sparse Hamiltonian simulation with optimal dependence on the maximum column Euclidean norm","arxiv_id":"2610.02030","primary_cat":"quant-ph","submitted_at":"2026-10-01T16:47:55+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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queries.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.63,"quantitative":true,"quantitative_p":0.98,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.96,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.04,"interpretation":0.0}},{"i":2,"p":0.66,"id":"s2","own":true,"role":"interpretation","text":"This removes the subpolynomial overhead in Low's algorithm [STOC 2019], replacing it with an additive logarithmic precision term.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.82,"main_claim_p":0.23,"quantitative":true,"quantitative_p":0.53,"role_probabilities":{"gap":0.01,"method":0.0,"result":0.06,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.27,"interpretation":0.66}},{"i":3,"p":0.61,"id":"s3","own":true,"role":"result","text":"For $d>1$ and $t\\Lambda\\ge\\log(2/\\epsilon)$, the bound matches the worst-case lower bound.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.78,"main_claim_p":0.19,"quantitative":true,"quantitative_p":0.97,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.61,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.39}},{"i":4,"p":0.33,"id":"s4","own":false,"role":"method","text":"A known spectral-norm upper bound may also be used in place of $\\Lambda$.","hedge":{"p":0.95,"label":"hedged_possibility"},"own_p":0.37,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.12,"role_probabilities":{"gap":0.0,"method":0.33,"result":0.24,"background":0.11,"limitation":0.07,"future_work":0.0,"contribution":0.18,"interpretation":0.07}},{"i":5,"p":0.95,"id":"s5","own":true,"role":"result","text":"The number of 1- and 2-qubit gates is linear in the query scale, up to oracle costs and polynomial overhead in the input bit lengths and logarithmic precision parameters.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.9,"main_claim_p":0.07,"quantitative":true,"quantitative_p":0.91,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.95,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.04,"interpretation":0.0}},{"i":6,"p":0.73,"id":"s6","own":true,"role":"result","text":"As applications, we obtain $O(\\kappa\\sqrt d\\,\\mathrm{polylog}(\\kappa/\\epsilon))$ queries for solving $d$-sparse quantum linear systems with $\\|A\\|\\le1$ and $\\|A^{-1}\\|\\le\\kappa$, under standard sparse and state-preparation access.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.08,"quantitative":true,"quantitative_p":0.98,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.73,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.25,"interpretation":0.02}},{"i":7,"p":0.66,"id":"s7","own":true,"role":"contribution","text":"We also give a gate-efficient implementation of black-box unitaries with at most $d$ nonzero entries per row and column using $O(\\sqrt d\\log(2/\\epsilon))$ queries, given sparse access to the unitary and its adjoint.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.06,"quantitative":true,"quantitative_p":0.98,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.34,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.66,"interpretation":0.0}},{"i":8,"p":0.55,"id":"s8","own":true,"role":"interpretation","text":"At constant error, the query bound is optimal and yields $\\Theta(\\sqrt N)$ queries for arbitrary $N\\times N$ unitaries, resolving the open question on black-box unitary implementation posed by Berry and Childs [QIC 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