Squeezing-free quantum gates for GKP codes

The Gottesman-Kitaev-Preskill (GKP) code is a promising candidate for the quantum error correction in the bosonic-mode-based quantum information processing. One major advantage of the GKP code is that all the logical Clifford gates are Gaussian and the only non-Gaussian resource we need is the GKP state itself. However, in many bosonic systems, especially for the optical platform, even the Gaussian squeezing gate like controlled-SUM gate is hard to implement, hindering the realization of the GKP CNOT gate.

To address this challenge, we propose new schemes of the teleportation-based GKP CNOT gate using only beam splitters and few squeezed-vacuum state or GKP state ancillas. To suppress the noise, we further implement the GKP error correction during the implementation of the CNOT gate, and compare schemes with different ancilla resources and decoding strategies. Our squeezing-free quantum gates for GKP codes will enable a fully passive linear-optical universal GKP gate operations.