Classical simulation and quantum resource theory of non-Gaussian optics

Understand

We propose efficient algorithms for classically simulating Gaussian unitaries and measurements applied to non-Gaussian initial states.

• The constructions are based on decomposing the non-Gaussian states into linear combinations of Gaussian states.
• We use an extension of the covariance matrix formalism to efficiently track relative phases in the superpositions of Gaussian states.
• We get an exact simulation algorithm, which costs quadratically with the number of Gaussian states required to represent the initial state, and an approximate simulation algorithm, which costs linearly with the $l_1$ norm of the coefficients associated with the superposition.