  We investigate two models for performing topological quantum gates with the
Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects. Topological one- and
two-qubit Abelian phases can be enacted with the AB effect using charge qubits,
whereas the AC effect can be used to perform all single-qubit gates (Abelian
and non-Abelian) for spin qubits. Possible experimental setups suitable for a
solid state implementation are briefly discussed.
