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

TL;DR

This paper explores implementing modular quadrature measurements using tunable photon-pressure coupling in circuit-QED, analyzing feasibility, expected squeezing, and error effects for GKP qubit preparation.

Contribution

It proposes a practical circuit-QED approach for modular quadrature measurements with estimates of achievable GKP squeezing and error impacts.

Findings

Feasible implementation of modular quadrature measurements in circuit-QED.

Estimated GKP squeezing achievable with the proposed protocol.

Analysis of photon loss and errors on squeezing performance.

Abstract

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.