2025/06/25 by Michael C D Tayler, Tayler, Michael C D, Mohamed Sabba +1 · 1 voice · 1 citation
Engineering · Physics and Astronomy · #FOS: Physical sciences #Gear and Bearing Dynamics Analysis #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.2506.20594
openalex publication_date 2025/06/25 · arxiv published 2025/06/25 · arxiv updated 2025/06/25 · openalex created_date 2025/10/09 · openalex updated_date 2026/07/31
We identify a cyclic property of rotation sequences involving piecewise displacements β about arbitrary axes in three dimensions. Specifically, when transformation to the toggling frame is applied successively m times, for β=2π/m the original sequence returns. This main result unites several families of rotation sequences used for error-tuned control across quantum technologies, from NMR and MRI to atomic clocks and atom-scale computing. For the widest class of cycle, m=2, we highlight sequence duality where every narrowband π-element sequence has a broadband π-element counterpart, and vice-versa. Higher cycles (m>2) connect to polyhedral models for error-tolerant sequence design, characterized by vertex axes with m-fold rotational symmetry. We derive original sequences and outline their applications to spin control and spin decoupling.