



01668nas a2200169   4500008004100000245006300041210006100104260001400165490000600179520118500185100002301370700002301393700001301416700001401429700001801443856003701461       2020                        eng d00aTime-dependent Hamiltonian simulation with L1-norm scaling0 aTimedependent Hamiltonian simulation with L1norm scaling  c4/20/20200 v43 a<p>The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation algorithms that exploit this intuition. For the case of sparse Hamiltonian simulation, the gate complexity scales with the L1 norm &int;t0dτ∥H(τ)∥max, whereas the best previous results scale with tmaxτ&isin;[0,t]∥H(τ)∥max. We also show analogous results for Hamiltonians that are linear combinations of unitaries. Our approaches thus provide an improvement over previous simulation algorithms that can be substantial when the Hamiltonian varies significantly. We introduce two new techniques: a classical sampler of time-dependent Hamiltonians and a rescaling principle for the Schrödinger equation. The rescaled Dyson-series algorithm is nearly optimal with respect to all parameters of interest, whereas the sampling-based approach is easier to realize for near-term simulation. By leveraging the L1-norm information, we obtain polynomial speedups for semi-classical simulations of scattering processes in quantum chemistry.</p>1 aBerry, Dominic, W.1 aChilds, Andrew, M.1 aSu, Yuan1 aWang, Xin1 aWiebe, Nathan  uhttps://arxiv.org/abs/1906.07115