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

Geometric phase gate on an optical transition for ion trap quantum computation