  Continuous-variable (CV) quantum information processing is a promising
candidate for large-scale fault-tolerant quantum computation. However, analysis
of CV quantum process relies mostly on direct computation of the evolution of
operators in the Heisenberg picture, and the features of CV space has yet to be
thoroughly investigated in an intuitive manner. One key ingredient for further
exploration of CV quantum computing is the construction of a computational
model that brings visual intuition and new tools for analysis. In this paper,
we delve into a graphical computational model, inspired by a similar model for
qubit-based systems called the ZX calculus, that enables the representation of
arbitrary CV quantum process as a simple directed graph. We demonstrate the
utility of our model as a graphical tool to comprehend CV processes intuitively
by showing how equivalences between two distinct quantum processes can be
proven as a sequence of diagrammatic transformations in certain cases. We also
examine possible applications of our model, such as measurement-based quantum
computing, characterization of Gaussian and non-Gaussian processes, and circuit
optimization.
