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

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.