Variational quantum algorithms for nonlinear problems

Michael Lubasch, Jae Woo Joo, Pierre Moinier, Martin Kiffner, Dieter Jaksch

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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 Schrödinger 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.
Original languageEnglish
Article number010301(R)
JournalPhysical Review A
Issue number1
Publication statusPublished - 6 Jan 2020


  • Quantum Simulation
  • quantum computing
  • RCUK
  • EP/K038311/1
  • EP/M013243/1


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