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

Continuous-variable quantum-computing 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. (paper)