Cycle Qubits: Theory, Gate Implementation, Calibration, and Supplementary Perspectives

This publication presents a series of four complementary documents on the concept of Cycle Qubits: Theory – the fundamental idea of encoding logical states on a quantum limit cycle stabilized by contradictory processes of pumping and damping, with analytical models and potential for natural error autocorrection. Gate Implementation – analytical control equations and timing estimates for $R_Z$, $X$, Hadamard, and CPHASE/CZ gates. Calibration Procedures – practical step-by-step methods to measure the cycle radius, amplitude stability, phase diffusion, drive maps, detuning calibration, two-qubit coupling $J$, as well as benchmarking and error bias analysis. Supplementary Perspectives – selected literature references and open research questions that position Cycle Qubits in the wider landscape of nonlinear dynamics, bosonic codes, and quantum error correction. The goal of this publication is not to claim a final theory, but to provide hypotheses, analytical tools, and questions that may inspire further research. The work arose from my research questions and analyses developed with the assistance of an artificial intelligence system. I am fully aware of both the potential and the limitations of current AI technologies, and I share these materials openly as an invitation to discussion and critical analysis.