Infleqtion: 2 Logical Qubits with Gottesman Protocol Complete Realization

Infleqtion demonstrated 2 logical qubits on a cesium neutral-atom hexagonal lattice using the [[4,2,2]] error-detection code, achieving the first complete realization of the Gottesman 2016 benchmarking protocol and the first application to materials science — with 15× error reduction over physical qubits.

In December 2025, Infleqtion implemented the [[4,2,2]] error-detection code on a cesium (Cs) neutral-atom quantum computer — encoding 4 physical qubits into 2 logical qubits (code distance d=2). A total of 6 physical qubits including flag qubits were arranged in a hexagonal lattice at 6 µm spacing. The system achieved a median CZ gate fidelity of 99.48% and a GR gate fidelity of 99.96%, with circuits optimized using the SUPERSTAQ compiler combined with NVIDIA CUDA-Q GPU acceleration.

Three key achievements were demonstrated:

First complete realization of the Gottesman 2016 fault-tolerant benchmarking protocol (3 initial states × 147 random circuits): logical qubit TVD of 0.7% vs. physical qubit TVD of 10.5% for |00⟩ input — a 15× error reduction.
Logical Bell state fidelity of 99.33%, compared to physical Bell fidelity of 91.71% — a 12.4× improvement.
First materials science application with error-detection codes: ground-state preparation of the Single Impurity Anderson Model (SIAM) using the [[4,2,2]] code achieved a 6× relative error reduction over bare physical qubits.

These results demonstrate that the [[4,2,2]] code lies on a path toward C4/C6 concatenated codes for universal fault-tolerant quantum computation, and that small-scale logical qubits already deliver practical accuracy improvements for near-term applications.