Exact and approximate continuous-variable gate decompositions

We gather and examine in detail gate decomposition techniques for continuous-variable quantum computers and also introduce some new techniques which expand on these methods. Both exact and approximate decomposition methods are studied and gate counts are compared for some common operations. While each having distinct advantages, we find that exact decompositions have lower gate counts whereas approximate techniques can cover decompositions for all continuous-variable operations but require significant circuit depth for a modest precision.

Automated summary

Exact decomposition methods have lower gate counts, while approximate techniques cover decompositions for all operations but require significant circuit depth.