Sparse Hamiltonian simulation with optimal dependence on the maximum column Euclidean norm

We give a quantum algorithm for simulating a $d$-sparse Hermitian Hamiltonian $H$, assuming a known upper bound $Λ$ on its maximum column Euclidean norm $\|H\|_{1\to2}$. For $tΛ\ge1/2$, simulation with operator-norm error $ε$ uses \[ O\!\left(tΛ\sqrt d+\sqrt d\log(2/ε)\right) \] sparse-oracle quer