Experimental demonstration of quantum-state tomography and qubit-qubit interactions for rare-earth-metal-ion-based solid-state qubits

We report on the implementation of quantum state tomography for an ensemble of ${\text{Eu}}^{3+}$ dopant ions in a ${\mathrm{Y}}_2{\text{SiO}}_5$ crystal. The tomography was applied to a qubit based on one of the ions’ optical transitions. The qubit was manipulated using optical pulses and measurements were made by observing the optical free induction in a phase sensitive manner. Fidelities of $>90\%$ for the combined preparation and measurement process were achieved. Interactions between the ions due to the change in the ions’ permanent electric dipole moment when excited optically were also measured. In light of these results, the ability to do multiqubit quantum computation using this system is discussed.