Realistic GKP stabilizer states enable universal quantum computation

• URL: http://arxiv.org/abs/2511.03874v1
• Date: Wed, 05 Nov 2025 21:42:54 GMT
• Title: Realistic GKP stabilizer states enable universal quantum computation
• Authors: Fariba Hosseinynejad, Pavithran Iyer, Guillaume Dauphinais, David L. Feder,
• Abstract summary: Physical Gottesman-Kitaev-Preskill (GKP) states are inherently noisy as ideal ones would require infinite energy.<n>This work demonstrates that imperfect GKP stabilizer states can be leveraged in order to apply non-Clifford gates using only linear optical elements.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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