Numerical Analysis and Scientific Computing Seminar | Di Fang, Time-dependent Hamiltonian Simulation: Quantum Algorithm and Superconvergence | Applied Mathematics

Zoom (Please contact ddelreyfernandez@uwaterloo.ca for meeting link)

Speaker

Di Fang Assistant Professor, Department of Mathematics, Duke University

Title

Time-dependent Hamiltonian Simulation: Quantum Algorithm and Superconvergence

Abstract

Hamiltonian simulation becomes more challenging as the underlying unitary becomes more oscillatory. In such cases, an algorithm with commutator scaling and a weak dependence, such as logarithmic, on the derivatives of the Hamiltonian is desired. We introduce a new time-dependent Hamiltonian simulation algorithm based on the Magnus series expansion that exhibits both features. Importantly, when applied to unbounded Hamiltonian simulation in the interaction picture, we prove that the commutator in the second-order algorithm leads to a surprising fourth-order superconvergence, with an error preconstant independent of the number of spatial grids. The proof of superconvergence is based on semiclassical analysis that is of independent interest.