Abstract
Bias-tailored quantum error correcting codes (QECCs) offer a higher error threshold than standard QECCs and have the potential to achieve lower logical errors with less space overhead. The spin-cat qubit, encoded in a large nuclear spin- system, is a promising candidate for bias-tailored QECCs. Yet its feasibility is hindered by the difficulty of performing fast covariant SU(2) rotation with arbitrary rotation angles for nuclear spins and by a lack of noise characterization for gate operations in neutral atom platforms. Here we demonstrate single-qubit controls of spin-cat qubits with nuclear spin in an optical tweezer array. We implement a covariant SU(2) rotation and non-linear rotations by optical beams and achieve an averaged single-Clifford gate fidelity of . The measurement of the coherence time and spin relaxation time shows that the idling error becomes increasingly biased toward dephasing errors as the magnitude of the encoded sublevel increases. Furthermore, we benchmark the noise bias of rank-preserving gates on spin-cat qubits, demonstrating a finite bias of , in contrast to the case of the two-level system in , which shows no bias within the experimental uncertainty. Our work demonstrates the feasibility of spin-cat qubits for realizing bias-tailored QECCs, paving the way for achieving hardware-efficient quantum error correction.