  Much progress has been made in the field of quantum computing using
continuous variables over the last couple of years. This includes the
generation of extremely large entangled cluster states (10,000 modes, in fact)
as well as a fault tolerant architecture. This has led to the point that
continuous-variable quantum computing can indeed be thought of as a viable
alternative for universal quantum computing. With that in mind, we present a
new algorithm for continuous-variable quantum computers which gives an
exponential speedup over the best known classical methods. Specifically, this
relates to efficiently calculating the scattering amplitudes in scalar bosonic
quantum field theory, a problem that is believed to be hard using a classical
computer. Building on this, we give an experimental implementation based on
cluster states that is feasible with today's technology.
