All you need is Trotter

Abstract

The work here enables linear cost-scaling with evolution time $t$ while keeping $\mathrm{polylog}(1/\hat{I}\mu )$ scaling and no extra block-encoding qubits, where $\hat{I}\mu$ 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.

17 pages