Ze-Cheng Li

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 $\Lambda$ on its maximum column Euclidean norm $\|H\|_{1\to2}$. For $t\Lambda\ge1/2$, simulation with operator-norm error $\epsilon$ uses \[ O\!\left(t\Lambda\sqrt d+\sqrt d\log(2/\epsilon)\right) \] sparse-o...