Cycle Qubits: Limit-Cycle Architecture as an Alternative for Stabilized Logical Qubits

I propose the concept of the Cycle Qubit, where the logical state is encoded on a quantum limit cycle maintained by contradictory processes of pumping and damping, together with phase rotation. Unlike static cat qubits, this architecture relies on dynamic equilibrium of opposing processes as the mechanism of amplitude stabilization and phase control. I analyze a Lindblad model (quantum van der Pol oscillator), derive conditions for the attractor radius, discuss logical gate protocols, and highlight potential advantages and limitations. The aim is not to provide a final theory but to ask whether such an approach can inspire further exploration of natural error autocorrection in quantum computing.