Realizing modular quadrature measurements via a tunable photon-pressure coupling in circuit-QED

Understand

One of the most direct preparations of a Gottesman-Kitaev-Preskill qubit in an oscillator uses a tunable photon-pressure (also called optomechanical) coupling of the form $g \hat{q} a^{\dagger} a$, enabling to imprint the modular value of the position $\hat{q}$ of one oscillator onto the state of an ancilla oscillator.

• We analyze the practical feasibility of executing such modular quadrature measurements in a parametric circuit-QED realization of this coupling.
• We provide estimates for the expected GKP squeezing induced by the protocol and discuss the effect of photon loss and other errors on the resulting squeezing.