  Using discrete and continuous variable subsystems, hybrid approaches to
quantum information could enable more quantum computational power for the same
physical resources. Here, we propose a hybrid scheme that can be used to
generate the necessary Gaussian and non-Gaussian operations for universal
continuous variable quantum computing in trapped ions. This scheme utilizes two
linear spin-motion interactions to generate a broad set of non-linear effective
spin-motion interactions including one and two mode squeezing, beam splitter,
and trisqueezing operations in trapped ion systems. We discuss possible
experimental implementations using laser-based and laser-free approaches.
