



@article {3197,
	title = {Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schr{\"o}dinger Equation},
	journal = {Quantum},
	volume = {6},
	year = {2022},
	month = {apr},
	pages = {690},
	abstract = {<p>We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm that is both insensitive to the rapid changes of the time-dependent Hamiltonian and exhibits commutator scaling. Our method can be used for efficient Hamiltonian simulation in the interaction picture. In particular, we demonstrate that for the simulation of the Schr{\"o}dinger equation, our method exhibits superconvergence and achieves a surprising second order convergence rate, of which the proof rests on a careful application of pseudo-differential calculus. Numerical results verify the effectiveness and the superconvergence property of our method.</p>},
	doi = {10.22331/q-2022-04-15-690},
	url = {https://arxiv.org/abs/2111.03103v2},
	author = {Dong An and Di Fang and Lin Lin}
}
