  We propose a geometric phase gate of two ion qubits that are encoded in two
levels linked by an optical dipole-forbidden transition. Compared to hyperfine
geometric phase gates mediated by electric dipole transitions, the gate has
many interesting properties, such as very low spontaneous emission rates,
applicability to magnetic field insensitive states, and use of a co-propagating
laser beam geometry. We estimate that current technology allows for
infidelities of around 10$^{-4}$.
