We propose a novel measurement-free scheme for stabilizing a spin-oscillator hybrid qubit via autonomous quantum error correction. The engineered Lindbladian renders the code space into an attractive steady-state subspace, realized by coupling the storage mode to a rapidly cooled bath through a controlled beam-splitter and spin-dependent displacement interactions. The continuous variable-discrete variable hybrid approach to autonomous quantum error correction preserves the hardware efficiency of conventional dissipation engineering while simplifying the required system-bath coupling. The construction is compatible with simple logical gates and leverages primitives already demonstrated in experimental platforms, such as trapped-ion systems, suggesting a practical route to hardware-efficient, noise-biased logical qubits without repeated syndrome measurements and feedforward.
@article{arxiv.2604.11145,
title = {Autonomous Quantum Error Correction of Spin-Oscillator Hybrid Qubits},
author = {Sungjoo Cho and Ju-yeon Gyhm and Hyukjoon Kwon and Hyunseok Jeong},
journal= {arXiv preprint arXiv:2604.11145},
year = {2026}
}