Abstract
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 lead 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 known 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.
