# Encoding qubits into oscillators with atomic ensembles and squeezed light

## TL;DR

This paper proposes a method to generate optical GKP-encoded qubits by coupling atomic ensembles with squeezed light, enabling fault-tolerant quantum computing with Gaussian operations and heralded state preparation.

## Contribution

It introduces a novel approach to produce GKP states using atomic ensembles and squeezed light, addressing the challenge of state generation in quantum error correction.

## Key findings

- Heralded generation of GKP states demonstrated
- Resource analysis shows feasible spin and squeezing requirements
- Proposed implementation uses Faraday-based quantum non-demolition interaction

## Abstract

The Gottesman-Kitaev-Preskill (GKP) encoding of a qubit within an oscillator provides a number of advantages when used in a fault-tolerant architecture for quantum computing, most notably that Gaussian operations suffice to implement all single- and two-qubit Clifford gates. The main drawback of the encoding is that the logical states themselves are challenging to produce. Here we present a method for generating optical GKP-encoded qubits by coupling an atomic ensemble to a squeezed state of light. Particular outcomes of a subsequent spin measurement of the ensemble herald successful generation of the resource state in the optical mode. We analyze the method in terms of the resources required (total spin and amount of squeezing) and the probability of success. We propose a physical implementation using a Faraday-based quantum non-demolition interaction.