  Numerical simulation of continuous variable quantum state preparation is a
necessary tool for optimization of existing quantum information processing
protocols. A powerful instrument for such simulation is the numerical
computation in the Fock state representation. It unavoidably uses an
approximation of the infinite-dimensional Fock space by finite complex vector
spaces implementable with classical digital computers. In this approximation we
analyze the accuracy of several currently available methods for computation of
the truncated coherent displacement operator. To overcome their limitations we
propose an alternative with improved accuracy based on the standard matrix
exponential. We then employ the method in analysis of non-Gaussian state
preparation scheme based on coherent displacement of a two mode squeezed vacuum
with subsequent photon counting measurement. We compare different detection
mechanisms, including avalanche photodiodes, their cascades, and photon number
resolving detectors in the context of engineering non-linearly squeezed cubic
states and construction of qubit-like superpositions between vacuum and single
photon states.
