Realizing modular quadrature measurements via a tunable photon-pressure coupling in circuit QED
Daniel Weigand, Barbara M. Terhal
Abstract
One of the most direct preparations of a Gottesman-Kitaev-Preskill (GKP) qubit in an oscillator uses a tunable photon-pressure (also called optomechanical) coupling of the form $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{q}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{b}}^{\ifmmode\dagger\else\textdagger\fi{}}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{b}$, enabling us to imprint the modular value of the position $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{q}$ 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.