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Numerical simulation of continuous variable quantum state preparation is anecessary tool for optimization of existing quantum information processingprotocols. A powerful instrument for such simulation is the numericalcomputation in the Fock state representation. It unavoidably uses anapproximation of the infinite-dimensional Fock space by finite complex vectorspaces implementable with classical digital computers. In this approximation weanalyze the accuracy of several currently available methods for computation ofthe truncated coherent displacement operator. To overcome their limitations wepropose an alternative with improved accuracy based on the standard matrixexponential. We then employ the method in analysis of non-Gaussian statepreparation scheme based on coherent displacement of a two mode squeezed vacuumwith subsequent photon counting measurement. We compare different detectionmechanisms, including avalanche photodiodes, their cascades, and photon numberresolving detectors in the context of engineering non-linearly squeezed cubicstates and construction of qubit-like superpositions between vacuum and singlephoton states.

Taming numerical errors in simulations of continuous variable non-Gaussian state preparation