Variational quantum algorithms for nonlinear problems - Lubasch, M; Joo, J; Moinier, P; Kiffner, M; Jaksch, D (American Physical Society, 2020)
We show that nonlinear problems including nonlinear partial di↵erential equations can be e- ciently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat nonlinearities eciently and by introducing tensor networks as a programming paradigm. The key concepts of the algorithm are demonstrated for the nonlinear Schr¨odinger equation as a canonical example. We numerically show that the variational quantum ansatz can be exponentially more ecient than matrix product states and present experimental proof-of-principle results obtained on an IBM Q device.