  The processing of quantum information always has a cost in terms of physical
resources such as energy or time. Determining the resource requirements is not
only an indispensable step in the design of practical devices - the resources
need to be actually provided - but may also yield fundamental constraints on
the class of processes that are physically possible. Here we study how much
energy is required to implement a desired unitary gate on a quantum system with
a non-trivial energy spectrum. We derive a general lower bound on the energy
requirement, extending the main result of Ref. [1] from finite dimensional
systems to systems with unbounded Hamiltonians. Such an extension has immediate
applications in quantum information processing with optical systems, and allows
us to provide bounds on the energy requirement of continuous variable quantum
gates, such as displacement and squeezing gates.
