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arXiv · 2511.03874

Realistic Gottesman-Kitaev-Preskill stabilizer states enable universal quantum computation

Fariba Hosseinynejad·Pavithran Iyer·Guillaume Dauphinais·David L. Feder
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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.

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Fariba Hosseinynejad, Pavithran Iyer, Guillaume Dauphinais, David L. Feder. 2025-11-05. Realistic Gottesman-Kitaev-Preskill stabilizer states enable universal quantum computation. https://doi.org/10.1103/ffln-vd4x

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