Quantum algorithm for nonlinear differential equations

• DOI: 10.48550/arxiv.2011.06571
• Publication Date: 2020-01-01
• Authors: Lloyd, Seth; De Palma, Giacomo; Gokler, Can; Kiani, Bobak; Liu, Zi-Wen; Marvian, Milad; Tennie, Felix; Palmer, Tim
• Keywords: Quantum Physics; 0103 physical sciences; FOS: Physical sciences; Chaotic Dynamics (nlin.CD); Nonlinear Sciences - Chaotic Dynamics; Quantum Physics (quant-ph); 01 natural sciences

Quantum computers are known to provide an exponential advantage over classical computers for the solution of linear differential equations in high-dimensional spaces. Here, we present a quantum algorithm for the solution of nonlinear differential equations. The quantum algorithm provides an exponential advantage over classical algorithms for solving nonlinear differential equations. Potential applications include the Navier-Stokes equation, plasma hydrodynamics, epidemiology, and more.<br/>13 pages, plain TeX, replaced to correct an error in equation 10 and to add a section on normalization to the supplementary material<br/>