  The simulation of large nonlinear dynamical systems, including systems
generated by discretization of hyperbolic partial differential equations, can
be computationally demanding. 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 describe a method for mapping any
finite nonlinear dynamical system to an infinite linear dynamical system
(embedding) and detail three specific cases of this method that correspond to
previously-studied mappings. Then we explore an approach for approximating the
resulting infinite linear system with finite linear systems (truncation). Using
a number of qubits only logarithmic in the number of variables of the nonlinear
system, a quantum computer could simulate truncated systems to approximate
output quantities if the nonlinearity is sufficiently weak. Other aspects of
the computational efficiency of the three detailed embedding strategies are
also discussed.
