Due to inhomogeneous broadening, the absorption lines of rare-earth-ion
dopands in crystals are many order of magnitudes wider than the homogeneous
linewidths. Several ways have been proposed to use ions with different
inhomogeneous shifts as qubit registers, and to perform gate operations between
such registers by means of the static dipole coupling between the ions.
In this paper we show that in order to implement high-fidelity quantum gate
operations by means of the static dipole interaction, we require the
participating ions to be strongly coupled, and that the density of such
strongly coupled registers in general scales poorly with register size.
Although this is critical to previous proposals which rely on a high density of
functional registers, we describe architectures and preparation strategies that
will allow scalable quantum computers based on rare-earth-ion doped crystals.Comment: Submitted to Phys. Rev.