# Simulating realistic non-Gaussian state preparation

## TL;DR

This paper introduces a faster algorithm for simulating non-Gaussian state preparation in photonic systems, enabling exploration of loss effects and identifying feasible experimental regimes for non-Gaussian state generation.

## Contribution

A novel, efficient algorithm for calculating loop hafnians to simulate non-Gaussian state preparation under photon loss conditions.

## Key findings

- Non-Gaussian states are fragile to photon loss.
- Certain loss parameters still allow for non-zero non-Gaussianity.
- The algorithm improves simulation speed over previous methods.

## Abstract

We consider conditional photonic non-Gaussian state preparation using multimode Gaussian states and photon-number-resolving detectors in the presence of photon loss. While simulation of such state preparation is often computationally challenging, we show that obtaining the required multimode Gaussian state Fock matrix elements can be reduced to the computation of matrix functions known as loop hafnians, and develop a tailored algorithm for their calculation that is faster than previously known methods. As an example of its utility, we use our algorithm to explore the loss parameter space for three specific non-Gaussian state preparation schemes: Fock state heralding, cat state heralding, and weak cubic-phase state heralding. We confirm that these schemes are fragile with respect to photon loss, yet find that there are regions in the loss parameter space that are potentially accessible in an experimental setting which correspond to heralded states with non-zero non-Gaussianity.