Experimental quantum-state tomography of a solid-state qubit

Quantum-state tomography is used to characterize the state of an ensemble based qubit implemented through two hyperfine levels in Pr³⁺ ions, doped into a Y₂SiO₅ crystal. We experimentally verify that single-qubit rotation errors due to inhomogeneities of the ensemble can be suppressed using the Roos-M{}lmer dark-state scheme [Roos and M{}lmer, Phys. Rev. A 69, 022321 (2004)] Fidelities above $>90%$, presumably limited by excited state decoherence, were achieved. Although not explicitly taken care of in the Roos-M{}lmer scheme, it appears that also decoherence due to inhomogeneous broadening on the hyperfine transition is largely suppressed.