# Non-Gaussian and Gottesman-Kitaev-Preskill state preparation by photon catalysis

## TL;DR

This paper proposes a theoretical method using photon catalysis to generate non-Gaussian states, including GKP states, which are crucial for scalable continuous-variable quantum computing.

## Contribution

It introduces photon catalysis as a new approach for non-Gaussian state engineering, enabling the creation of GKP and other complex quantum states.

## Key findings

- Photon catalysis can produce displaced single-photon states.
- Photon catalysis can generate M-symmetric superpositions of squeezed vacuum.
- State breeding can enlarge SSV states and facilitate GKP state production.

## Abstract

Continuous-variable quantum-computing (CVQC) is the most scalable implementation of QC to date but requires non-Gaussian resources to allow exponential speedup and quantum correction, using error encoding such as Gottesman-Kitaev-Preskill (GKP) states. However, GKP state generation is still an experimental challenge. We show theoretically that photon catalysis, the interference of coherent states with single-photon states followed by photon-number-resolved detection, is a powerful enabler for non-Gaussian quantum state engineering such as exactly displaced single-photon states and $M$-symmetric superpositions of squeezed vacuum (SSV), including squeezed cat states ($M=2$). By including photon-counting based state breeding, we demonstrate the potential to enlarge SSV states and produce GKP states.