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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\u00f6dinger 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.<\/jats:p>","DOI":"10.22331\/q-2022-04-15-690","type":"journal-article","created":{"date-parts":[[2022,4,15]],"date-time":"2022-04-15T11:36:51Z","timestamp":1650022611000},"page":"690","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":36,"title":["Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schr\u00f6dinger Equation"],"prefix":"10.22331","volume":"6","author":[{"given":"Dong","family":"An","sequence":"first","affiliation":[{"name":"Joint Center for Quantum Information and Computer Science (QuICS), University of Maryland, College Park, MD 20742, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Di","family":"Fang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of California, Berkeley, CA 94720, USA"},{"name":"Simons Institute for the Theory of Computing, University of California, Berkeley, CA 94720, USA"},{"name":"Challenge Institute for Quantum Computation, University of California, Berkeley, CA 94720, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of California, Berkeley, CA 94720, USA"},{"name":"Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA"},{"name":"Challenge Institute for Quantum Computation, University of California, Berkeley, CA 94720, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2022,4,15]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"T. 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