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

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.

Automated summary

Numerical simulation of continuous variable quantum state preparation is essential for optimizing quantum information processing protocols. This study presents a powerful tool for such simulations using Fock state representation and numerical computation. The accuracy of several methods for computing the truncated coherent displacement operator is analyzed in an approximation of the infinite-dimensional Fock space by finite complex vector spaces. An alternative method with improved accuracy, based on the standard matrix exponential, is proposed. The method is then applied to analyze non-Gaussian state preparation schemes using coherent displacement of a two mode squeezed vacuum and photon counting measurement. Different detection mechanisms, including avalanche photodiodes, their cascades, and photon number resolving detectors, are compared for engineering non-linearly squeezed cubic states and constructing qubit-like superpositions.