Unbounded Hamiltonian Simulation: Quantum Algorithm and Superconvergence
Abstract: Simulation of quantum dynamics, emerging as the original motivation for quantum computers, is widely viewed as one of the most important applications of a quantum computer. Recent years have witnessed tremendous progress in developing and analyzing quantum algorithms for Hamiltonian simulation of bounded operators. However, many scientific and engineering problems require the efficient treatment of unbounded operators, which pose additional challenges, often arising from the discretization of differential operators. Such applications include molecular dynamics, electronic structure, quantum differential equations solver and quantum optimization. We will introduce some recent progresses in quantum algorithms for efficient unbounded Hamiltonian simulation, including Trotter type splitting and Magnus expansion based algorithms in the interaction picture. (The talk does not assume a priori knowledge on quantum computing.)
