  Although quantum computing holds promise to accelerate a wide range of
computational tasks, the quantum simulation of quantum dynamics as originally
envisaged by Feynman remains the most promising candidate for achieving quantum
advantage. A less explored possibility with comparably far-reaching
technological applicability is the quantum simulation of classical nonlinear
dynamics. Attempts to develop digital quantum algorithms based on the Koopman
von Neumann formalism have met with challenges because of the necessary
projection step from an infinite-dimensional Hilbert space to the
finite-dimensional subspace described by a collection of qubits. This
finitization produces numerical artifacts that limit solutions to very short
time horizons. In this paper we review continuous-variable quantum computing
(CVQC), which naturally avoids such obstacles, and a CVQC algorithm for KvN
simulation of classical nonlinear dynamics is advocated. In particular, we
present explicit gate synthesis for product-formula Hamiltonian simulation of
anharmonic vibrational dynamics.
