Variational quantum algorithms for nonlinear problems
Michael Lubasch, Jaewoo Joo, Pierre Moinier, Martin Kiffner, Dieter Jaksch
Abstract
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\"odinger 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.
Topics & Concepts
Nonlinear systemQuantumAlgorithmQuantum algorithmComputer scienceQuantum mechanicsPhysicsQuantum Computing Algorithms and ArchitectureQuantum Information and CryptographyNeural Networks and Reservoir Computing