



01292nas a2200157   4500008004100000245012000041210006900161260000800230300000800238490000600246520080400252100001301056700001301069700001301082856003901095       2022                        eng d00aTime-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schrödinger Equation0 aTimedependent Hamiltonian Simulation of Highly Oscillatory Dynam  capr  a6900 v63 a<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 Schrödinger 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>1 aAn, Dong1 aFang, Di1 aLin, Lin  uhttps://arxiv.org/abs/2111.03103v2