A framework for applying quantum computation to nonlinear dynamical systems
Alexander Engel, Graeme Smith, Scott Parker · arXiv (Cornell University) · 2020
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally extreme. Such systems are important in both fluid and kinetic computational plasma physics. This motivates exploring whether a future error-corrected quantum computer could perform these simulations more efficiently than any classical computer. We introduce a framework for mapping any finite nonlinear dynamical system to an infinite linear dynamical system (embedding) and detail three specific cases of this framework that correspond to previously-studied mappings. Additionally, we explore an approach for approximating the resulting infinite linear system with finite linear systems (truncation). A quantum computer could simulate these finite linear systems using a number of qubits that scales only logarithmically with the number of variables of the original nonlinear system. Computational efficiency of the three detailed embedding strategies is discussed.