All you need is Trotter

The work here enables linear cost-scaling with evolution time $t$ while keeping $\mathrm{p}\mathrm{o}\mathrm{l}\mathrm{y}\mathrm{l}\mathrm{o}\mathrm{g}(1\mathrm{/}\epsilon )$ scaling and no extra block-encoding qubits, where $\epsilon$ is the algorithmic error. This is achieved through product formulas, stable interpolation (Chebyshev), and to calculate the needed fractional queries, cardinal sine interpolation is used.