Mapping of a many-qubit state onto an oscillator using controlled displacements

TL;DR

This paper introduces a method to map multi-qubit states onto an oscillator using controlled displacements, enabling efficient GKP state preparation with linear growth in squeezing relative to qubits used.

Contribution

It extends controlled displacement interactions to multi-qubit systems and presents a circuit for encoding qudit superpositions into oscillator GKP states.

Findings

Deterministic mapping of qudit states onto an oscillator.

Efficient GKP state preparation with linear squeezing growth.

Protocol requires only two time-independent interactions.

Abstract

We extend the controlled displacement interaction between a qubit and a harmonic oscillator to the multi-qubit (qudit) case. We define discrete quadratures of the qudit and show how the qudit state can be displaced in these quadratures controlled by an oscillator quadrature. Using this interaction, a periodic repetition of the state encoded in the qudit, can be deterministically mapped onto the oscillator, which is initialized in a squeezed state. Based on this controlled displacement interaction, we present a full circuit that encodes quantum information in a superposition of qudit quadrature states, and successively prepares the oscillator in the corresponding superposition of approximate Gottesman-Kitaev-Preskill (GKP) states. This preparation scheme is found to be similar to phase estimation, with the addition of a disentanglement gate. Our protocol for GKP state preparation is efficient in the sense, that the set of qubits need only interact with the oscillator through two time-independent interactions, and in the sense that the squeeze factor (in dB) of the produced GKP state grows linearly in the number of qubits used.