Eliminating Qubit-Type Cross-Talk in the omg Protocol

The $omg$ protocol is a promising paradigm that uses multiple, application-specific, qubit subspaces within the Hilbert space of each single atom during quantum information processing. A key assumption for $omg$ operation is that a subspace can be accessed independently without deleterious effects on information stored in other subspaces. We find that intensity noise during laser-based quantum gates in one subspace can cause decoherence in other subspaces, potentially complicating $omg$ operation. We show, however, that a magnetic-field-induced vector light shift can be used to eliminate this source of decoherence. As this technique simply requires choosing a specific, magnetic field-dependent polarization for the gate lasers, it is straightforward to implement and potentially helpful for $omg$-based quantum technology.