Realistic Gottesman-Kitaev-Preskill stabilizer states enable universal quantum computation
Abstract
Physical Gottesman-Kitaev-Preskill (GKP) states are inherently noisy as ideal ones would require infinite energy. While this is typically considered as a deficiency to be actively corrected, this work demonstrates that imperfect GKP stabilizer states can be leveraged in order to apply non-Clifford gates using only linear optical elements. In particular, Gaussian operations on normalizable GKP states, combined with homodyne measurements, permit two key primitives: clean projection onto Pauli eigenstates in the normalizable GKP codespace, thereby implementing Clifford gates with high fidelity; and probabilistic projection of unmeasured modes onto non-Pauli eigenstates. These results demonstrate that normalizable GKP stabilizer states combined with Gaussian operations provide a practical framework for computational universality within the measurement-based model of quantum computation in a realistic continuous-variable setting.
Cite
@article{arxiv.2511.03874,
title = {Realistic Gottesman-Kitaev-Preskill stabilizer states enable universal quantum computation},
author = {Fariba Hosseinynejad and Pavithran Iyer and Guillaume Dauphinais and David L. Feder},
journal= {arXiv preprint arXiv:2511.03874},
year = {2026}
}