Electrical two-qubit gates within a pair of clock-qubit magnetic molecules

Enhanced coherence in HoW₁₀ molecular spin qubits has been demonstrated by use of clock-transitions (CTs). More recently it was shown that, while operating at the CTs, it was possible to use an electrical field to selectively address HoW₁₀ molecules pointing in a given direction, within a crystal that contains two kinds of identical but inversion-related molecules. Herein we theoretically explore the possibility of employing the electric field to effect entangling two-qubit quantum gates within a 2-qubit Hilbert space resulting from dipolar coupling of two CT-protected HoW₁₀ molecules in a diluted crystal. We estimate the thermal evolution of <em>T</em>₁, <em>T</em>₂, find that CTs are also optimal operating points from the point of view of phonons, and lay out how to combine a sequence of microwave and electric field pulses to achieve coherent control within a switchable two-qubit operating space between symmetric and asymmetric qubit states that are protected both from spin-bath and from phonon-bath decoherence. This two-qubit gate approach presents an elegant correspondence between physical stimuli and logical operations, meanwhile avoiding any spontaneous unitary evolution of the qubit states. Finally, we found a highly protected 1-qubit subspace resulting from the interaction between two clock molecules.