Continuous-angle logical rotations in the Steane code

Abstract:We experimentally demonstrate continuous-angle logical $Z$ rotations in the $[[7,1,3]]$ Steane code on the IonQ Forte trapped-ion processor. A round of the protocol applies a transversal physical $Z$ rotation by $\theta$, followed by Steane syndrome extraction and decoding, which induces a syndrome-dependent logical $Z$ rotation. We analytically derive the effect of dephasing noise on the logical rotation angle and logical dephasing rate. Using logical Ramsey interferometry, we observe coherent syndrome-dependent logical rotations from a single round of the protocol. We find that the logical channel reconstructed from process tomography is a noisy logical $Z$ rotation well explained by a dephasing model. We further implement a two-round protocol applying physical rotations $+\theta$ and $-\theta$, and observe cancellation of the total logical angle with low logical dephasing for repeated trivial syndromes. This constitutes a proof-of-principle demonstration of continuously tunable non-Clifford logical gates by transversal rotations and standard error correction in a small quantum code.

arXiv:2608.20676 [quant-ph]

(or arXiv:2608.20676v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.20676 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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