# Polynomial approximation of non-Gaussian unitaries by counting one photon at a time

## TL;DR

This paper introduces two methods for approximating non-Gaussian unitaries in continuous-variable quantum systems using single-photon counters, enabling better implementation of non-Gaussian operations crucial for quantum advantage.

## Contribution

The paper presents novel protocols for polynomial approximation of non-Gaussian unitaries using minimal non-Gaussian resources, specifically single-photon counters.

## Key findings

- Protocols achieve high fidelity in approximating target unitaries
- Effective for both Fock and coherent states
- Advances practical implementation of non-Gaussian quantum gates

## Abstract

In quantum computation with continous-variable systems, quantum advantage can only be achieved if some non-Gaussian resource is available. Yet, non-Gaussian unitary evolutions and measurements suited for computation are challenging to realize in the lab. We propose and analyze two methods to apply a polynomial approximation of any unitary operator diagonal in the amplitude quadrature representation, including non-Gaussian operators, to an unknown input state. Our protocols use as a primary non-Gaussian resource a single-photon counter. We use the fidelity of the transformation with the target one on Fock and coherent states to assess the quality of the approximate gate.