We examine continuous-variable gate teleportation using entangled states made from pure product states sent through a beamsplitter. We show that such states are Choi states for a (typically) non-unitary gate, and we derive the associated Kraus operator for teleportation, which can be used to realize non-Gaussian, non-unitary quantum operations on an input state. With this result, we show how gate teleportation is used to perform error correction on bosonic qubits encoded using the Gottesman-Kitaev-Preskill code. This result is presented in the context of deterministically produced macronode cluster states, generated by constant-depth linear optical networks, supplemented with a probabilistic supply of GKP states. The upshot of our technique is that state injection for both gate teleportation and error correction can be achieved without active squeezing operations -- an experimental bottleneck for quantum optical implementations.
@article{arxiv.2008.12791,
title = {Continuous-variable gate teleportation and bosonic-code error correction},
author = {Blayney W. Walshe and Ben Q. Baragiola and Rafael N. Alexander and Nicolas C. Menicucci},
journal= {arXiv preprint arXiv:2008.12791},
year = {2021}
}