The required set of operations for universal continuous-variable quantum
computation can be divided into two primary categories: Gaussian and
non-Gaussian operations. Furthermore, any Gaussian operation can be decomposed
as a sequence of phase-space displacements and symplectic transformations.
Although Gaussian operations are ubiquitous in quantum optics, their
experimental realizations generally are approximations of the ideal Gaussian
unitaries. In this work, we study different performance criteria to analyze how
well these experimental approximations simulate the ideal Gaussian unitaries.
In particular, we find that none of these experimental approximations converge
uniformly to the ideal Gaussian unitaries. However, convergence occurs in the
strong sense, or if the discrimination strategy is energy bounded, then the
convergence is uniform in the Shirokov-Winter energy-constrained diamond norm
and we give explicit bounds in this latter case. We indicate how these
energy-constrained bounds can be used for experimental implementations of these
Gaussian unitaries in order to achieve any desired accuracy.Comment: v3: 26 pages, 10 figures, final version accepted for publication in
Physical Review Researc
