Measurement-based generation and preservation of cat and grid states within a continuous-variable cluster state

TL;DR

This paper introduces a novel algorithm, PhANTM, that generates and stabilizes non-Gaussian quantum states like cat and GKP states within Gaussian CV cluster states, enhancing quantum error correction and computing.

Contribution

The paper presents PhANTM, a new method that uses photon-counting-assisted teleportation to embed and stabilize non-Gaussian states in Gaussian cluster states, enabling polynomial gate application.

Findings

PhANTM can reliably generate cat and GKP states within Gaussian cluster states.

The method stabilizes cat states against Gaussian noise.

Existing breeding protocols can be integrated into cluster state processing.

Abstract

We present an algorithm to reliably generate various quantum states critical to quantum error correction and universal continuous-variable (CV) quantum computing, such as Schr\"odinger cat states and Gottesman-Kitaev-Preskill (GKP) grid states, out of Gaussian CV cluster states. Our algorithm is based on the Photon-counting-Assisted Node-Teleportation Method (PhANTM), which uses standard Gaussian information processing on the cluster state with the only addition of local photon-number-resolving measurements. We show that PhANTM can apply polynomial gates and embed cat states within the cluster. This method stabilizes cat states against Gaussian noise and perpetuates non-Gaussianity within the cluster. We show that existing protocols for breeding cat states can be embedded into cluster state processing using PhANTM.