Short answer: The Gottesman-Kitaev-Preskill, or GKP, code stores a logical qubit in a single quantum harmonic oscillator instead of many physical qubits. A 2021 Nature Physics paper reports error correction of a GKP qubit in the motion of a single trapped ion with a threefold extension of the coherence time of logical states, and a 2025 Nature Physics paper reports an entangling gate on GKP logical qubits and a directly generated GKP Bell state. Both are trapped-ion laboratory demonstrations.
What the GKP code offers
The 2025 abstract says conventional fault-tolerant approaches encode one logical qubit in many physical qubits, and that the large physical-to-logical ratio of many codes outstrips the size of near-term devices. The GKP code, the authors say, offers hardware efficiency at the cost of more complex encoding, because it puts a logical qubit into a single quantum harmonic oscillator. The 2021 abstract describes it as a grid state encoding that allows small displacement errors to be corrected.
2021: error correction with one ion
The 2021 paper introduces and implements a dissipative map designed for physically realistic finite GKP codes. It performs error correction of a logical qubit encoded in the motion of a single trapped ion. The correction cycle has two rounds, which correct small displacements in position and momentum. The authors demonstrate an extension in the coherence time of logical states by a factor of three, using both square and hexagonal GKP codes. They note that the dissipative map can be viewed as a type of reservoir engineering that pumps into the manifold of highly non-classical GKP qubit states.
2025: an entangling gate
The 2025 paper builds on earlier GKP-encoded operations and realizes an entangling gate on GKP logical qubits. The experiments use an optimal control strategy that deterministically implements a universal set of energy-preserving logical gates on finite-energy GKP states encoded in the mechanical motion of a trapped ion. The authors also directly generate a GKP Bell state starting from vacuum. They say the approach is compatible with existing hardware architectures and show the potential of optimal control combined with advanced encodings. That last point is the authors' outlook, not a result.
A third source
An alphaXiv page for arXiv 1807.01033 was listed as a source, but its text was not readable here, so it is not described.
How the two papers relate
The 2021 result is about protecting a stored logical state, while the 2025 result is about operating on logical qubits, including an entangling gate. Together they cover two things a code needs: keeping information alive and computing with it. The abstracts do not combine them in one experiment, and each reports its own measure, a coherence time factor in one case and gate and state generation in the other.
Limits
Both results are small experiments in one platform, the motion of a trapped ion. A threefold coherence extension is a measured gain for logical states in that experiment, and the abstracts do not report a full error-corrected computation or scaling to many logical qubits.
FAQ
What is a GKP qubit?
A logical qubit encoded in a single quantum harmonic oscillator using a grid state, per the abstracts.
Why is it called hardware efficient?
It uses one oscillator instead of many physical qubits for each logical qubit.
What did the 2021 experiment show?
Error correction of a GKP qubit in a trapped ion's motion, with logical coherence extended by a factor of three.
What is new in 2025?
An entangling gate on GKP logical qubits and a GKP Bell state generated from vacuum.
Is this a fault-tolerant computer?
No. These are small trapped-ion experiments.
All field notes