Time-dependent Hamiltonian simulation with $L^1$-norm scaling

Understand

The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian.

• When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously.
• We develop quantum simulation algorithms that exploit this intuition.
• For sparse Hamiltonian simulation, the gate complexity scales with the $L^1$ norm $\int_{0}^{t}\mathrm{d}\tau\left\lVert H(\tau)\right\lVert_{\max}$, whereas the best previous results scale with $t\max_{\tau\in[0,t]}\left\lVert H(\tau)\right\lVert_{\max}$.