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We present a theoretical proposal for the implementation of geometric quantumcomputing 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 circuitcomposed of three SQUIDs and two superconducting islands with the charge statesencoding the logical states. We obtain a universal set of single-qubit gatesand implement a non-trivial two-qubit gate exploiting the mutual inductancebetween two neighboring circuits, allowing us to realize a fully geometricground-state quantum computing. The introduced paradigm for the implementationof geometric quantum computing is expected to be robust against environmentaleffects.

Ground-state geometric quantum computing in superconducting systems