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.
Highlights
AND MOTIVATIONBosonic quantum error correction encoding quantum information into oscillator space(s) has gained much experimental interest in the past few years (e.g., Refs. [1,2,3,4,5,6])
III A, we formally model the effect of the whole measurement protocol: In Fig. 2, we show the effect of the protocol using a coherent state with mean photon number n =
With respect to photon loss on the ancilla oscillator, an important possible advantage of the photon-pressure scheme proposed is that a single oscillator measurement is used instead of a sequence of qubit measurements, making it possible that the photon-pressure scheme is much faster
Summary
Bosonic quantum error correction encoding quantum information into oscillator space(s) has gained much experimental interest in the past few years (e.g., Refs. [1,2,3,4,5,6]). The original GKP paper [8] briefly suggested that a photon-pressure coupling between the target oscillator—in which the state is to be prepared—and an ancilla oscillator would be useful in this respect Through such an interaction, the ancilla oscillator acquires a frequency shift which depends on the quadrature qT. The aim here is to do a strong modular quadrature measurement, unlike some of the previous work [3,4,12] in which the measurement is built up from a sequence of weak measurements via coupling to ancilla qubits In the latter approach, the strong measurement—which is effectively a phase estimation or eigenvalue measurement of a unitary displacement operator—is obtained through a sequence of weak ancilla qubit measurements, each contributing at most 1 bit of phase information.
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