  We present a theoretical proposal for the implementation of geometric quantum
computing based on a Hamiltonian which has a doubly degenerate ground state.
Thus the system which is steered adiabatically, remains in the ground-state.
The proposed physical implementation relies on a superconducting circuit
composed of three SQUIDs and two superconducting islands with the charge states
encoding the logical states. We obtain a universal set of single-qubit gates
and implement a non-trivial two-qubit gate exploiting the mutual inductance
between two neighboring circuits, allowing us to realize a fully geometric
ground-state quantum computing. The introduced paradigm for the implementation
of geometric quantum computing is expected to be robust against environmental
effects.

Quantum Physics;Superconductivity