Towards the implementation of a logical CNOT gate between stabilized Gottesman-Kitaev-Preskill (GKP) qubits - Part 2of 2

Bosonic error correction is a promising candidate for the realization of quantum computation in the presence of noise. Recently, the Gottesman-Kitaev-Preskill (GKP) code with logical states realized as grid states encoded in an oscillator was prepared and stabilized using repeated interactions with an ancilla qubit at ETH and Yale. To realize universal computation with the GKP encoding, or to embed the GKP code in a higher-level layer of error correction, a logical two-qubit gate is needed, such that the full Clifford group can be implemented. Here, we focus on the realization of a logical controlled-NOT gate between GKP code words stabilized in a superconducting cavity. In the second part of this two-part talk, we discuss the design and implementation of the quadrature-quadrature interaction needed to engineer a logical two-qubit CNOT gate between stabilized GKP codes in cQED.