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Recent advances in quantum technologies have enabled the precise control ofsingle trapped molecules on the quantum level. Exploring the scope of these newtechnologies, we studied theoretically the implementation of qubits and clocktransitions in the spin, rotational, and vibrational degrees of freedom ofmolecular nitrogen ions including the effects of magnetic fields. The relevantspectroscopic transitions span six orders of magnitude in frequencyillustrating the versatility of the molecular spectrum for encoding quantuminformation. We identified two types of magnetically insensitive qubits withvery low ("stretched"-state qubits) or even zero ("magic" magnetic-fieldqubits) linear Zeeman shifts. The corresponding spectroscopic transitions arepredicted to shift by as little as a few mHz for an amplitude of magnetic-fieldfluctuations on the order of a few mG translating into Zeeman-limited coherencetimes of tens of minutes encoded in the rotations and vibrations of themolecule. We also found that the Q(0) line of the fundamental vibrationaltransition is magnetic-dipole allowed by interaction with the first excitedelectronic state of the molecule. The Q(0) transitions, which benefit fromsmall systematic shifts for clock operation and high sensitivity to a possiblevariation in the proton-to-electron mass ratio, were so far not considered insingle-photon spectra. Finally, we explored possibilities to coherently controlthe nuclear-spin configuration of N$_2^+$ through the magnetically enhancedmixing of nuclear-spin states.

From megahertz to terahertz qubits encoded in molecular ions: theoretical analysis of dipole-forbidden spectroscopic transitions in N$\mathbf{_2^+}$