Nullifiers of non-Gaussian cluster states through homodyne measurement

TL;DR

This paper introduces a practical method to certify non-Gaussian features in large-scale optical cluster states using homodyne measurements, advancing quantum computation capabilities.

Contribution

It extends Gaussian nullifiers to non-Gaussian states, providing a new framework for their characterization and experimental certification.

Findings

Derived non-Gaussian nullifiers for photon-subtracted squeezed states

Demonstrated the nullifiers experimentally from homodyne data

Provided a practical tool for certifying non-Gaussianity in optical cluster states

Abstract

In continuous variable optical platforms, large-scale Gaussian cluster states have already been demonstrated, but non-Gaussian resources are essential to achieve universality and fault tolerance in measurement-based quantum computation. However, characterizing and certifying non-Gaussian cluster states remains an outstanding challenge. Here, we introduce a general framework for the characterization of non-Gaussian cluster states based on non-Gaussian nullifiers, extending the widely used Gaussian nullifier concept. We show that these nullifiers can be directly evaluated from homodyne measurement data, making them experimentally accessible. As an illustration, we derive and experimentally demonstrate non-Gaussian nullifiers for photon-subtracted squeezed states. Our results provide a practical and operational tool for certifying quantum non-Gaussianity in large-scale optical cluster states.