  We show that nonlinear problems including nonlinear partial differential
equations can be efficiently solved by variational quantum computing. We
achieve this by utilizing multiple copies of variational quantum states to
treat nonlinearities efficiently and by introducing tensor networks as a
programming paradigm. The key concepts of the algorithm are demonstrated for
the nonlinear Schr\"{o}dinger equation as a canonical example. We numerically
show that the variational quantum ansatz can be exponentially more efficient
than matrix product states and present experimental proof-of-principle results
obtained on an IBM Q device.
