A multiplexed synthesizer for non-Gaussian photonic quantum state generation

Disposing of simple and efficient sources for photonic states with non-classical photon statistics is of paramount importance for implementing quantum computation and communication protocols. In this work, we propose an innovative approach that drastically simplifies the preparation of non-Gaussian states as compared to previous proposals, by taking advantage from the multiplexing capabilities offered by modern quantum photonics tools. Our proposal is inspired by iterative protocols, where multiple resources are combined one after the other for obtaining high-amplitude complex output states. Here, conversely, a large part of the protocol is performed in parallel, by using a single projective measurement along a mode which partially overlaps with all the input modes. We show that our protocol can be used to generate high-quality and high-amplitude Schr\"odinger cat states as well as more complex states such as error-correcting codes. Remarkably, our proposal can be implemented with experimentally available resources, highlighting its straightforward feasibility.