  We propose a scheme to implement Controlled Not-gate for topological qubits
in a quantum-dot-Majorana-fermion hybrid system. Quantum information is encoded
on pairs of Majorana fermions, which live on the the interface between
topologically trivial and nontrivial sections of a quantum nanowire deposited
on an s-wave superconductor. A measurement-based two-qubit Controlled-Not gate
is produced with the help of parity measurements assisted by the quantum-dot
and followed by prescribed single-qubit gates. The parity measurement, on the
quantum-dot and a topological qubit, is achieved by the Aharonov-Casher effect.
