All you need is Trotter
Gumaro Rendon · arXiv (Cornell University) · 2023
The work here enables linear cost-scaling with evolution time $t$ while keeping ${\rm polylog} (1/ε)$ scaling and no extra block-encoding qubits, where $ε$ 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.