Qubit States Based on Fractional Vortices in $0-\pi$ Josephson Junctions

We investigate the static properties of $0-\pi$ Josephson junctions and their potential application as superconducting qubits. We show that fractional vortex and fractional antivortex configurations give rise to a bistable free-energy landscape with stable minima corresponding to topologically distinct fractional-vortex states. In the long-junction limit the two configurations correspond to stable equilibrium states, whereas in the short-junction limit the reduced barrier suggests enhanced quantum tunneling and hybridization between them. These results suggest that $0-\pi$ Josephson junctions may provide a physically meaningful platform for qubit-like two-level dynamics, provided that a finite tunneling amplitude exists between the fractional-vortex and fractional-antivortex states.