  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.
