Sparse Hamiltonian simulation with optimal dependence on the maximum column Euclidean norm
This work presents a quantum algorithm to simulate a d-sparse Hermitian Hamiltonian H using sparse-oracle queries that optimally depend on its maximum column Euclidean norm ($\|H\|_1\to2$). The method achieves query complexity of $O( au + rac{\sqrt{d}}{2} \log \frac{2}{\epsilon})$, which simplifies to $O(\tau)$ when the time parameter is large enough. This establishes a worst-case optimal bound for Hamiltonian simulation, resolving open questions about efficient black-box unitary implementation.