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

TL;DR

This paper shows that noisy, realistic GKP stabilizer states combined with Gaussian operations enable universal quantum computation by implementing Clifford and non-Clifford gates through measurement-based methods.

Contribution

It introduces a practical approach to achieve universal quantum computation using imperfect GKP states and Gaussian operations without requiring ideal, infinite-energy states.

Findings

Gaussian operations and homodyne measurements enable high-fidelity Clifford gates.

Probabilistic projection onto non-Pauli states allows non-Clifford gates.

Normalizable GKP states facilitate measurement-based universal quantum computing.

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.