Variational quantum algorithms for nonlinear problems

By Michael Lubasch, Jaewoo Joo, Pierre Moinier, Martin Kiffner, Dieter Jaksch. Physical Review A, 2019

351 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/d28981ca20c753010a0d3fd53f056826fecc5ac1

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Citations in the corpus

Variational quantum algorithms (2020, methodology): “To address this, a VQA for such non-linear problems was proposed in [122].”
Quantum computing with neutral atoms (2020, methodology): “ large-scale simulations for reliable weather forecasts, computational uid dynamics in aeronautics, or even nance. An algorithm was recently proposed to solve non-linear partial dierential equations [23] using a quantum accelerator within a variational procedure. The ecient implementation proposed i”