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arXiv:0708.0764 · Physical Review A

Experimental quantum-state tomography of a solid-state qubit

Lars Rippe, Brian Julsgaard, Andreas Walther, Ying Lin Yan, Stefan Kröll

Published Feb 7, 2008• 83 citations
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Abstract

Quantum-state tomography is used to characterize the state of an ensemble based qubit implemented through two hyperfine levels in ${\mathrm{Pr}}^{3+}$ ions, doped into a ${\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}$ crystal. We experimentally verify that single-qubit rotation errors due to inhomogeneities of the ensemble can be suppressed using the Roos-M\o{}lmer dark-state scheme [Roos and M\o{}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\o{}lmer scheme, it appears that also decoherence due to inhomogeneous broadening on the hyperfine transition is largely suppressed.

DOI
10.1103/physreva.77.022307

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Quantum-state tomography is used to characterize the state of an ensemble based qubit implemented through two hyperfine levels in Pr3+{\mathrm{Pr}}^{3+}Pr3+ ions, doped into a Y2SiO5{\mathrm{Y}}_{2}\mathrm{Si}{\mathrm{O}}_{5}Y2​SiO5​ crystal. We experimentally verify that single-qubit rotation errors due to inhomogeneities of the ensemble can be suppressed using the Roos-M\o{}lmer dark-state scheme [Roos and M\o{}lmer, Phys. Rev. A 69, 022321 (2004)] Fidelities above >90>90%>90, presumably limited by excited state decoherence, were achieved. Although not explicitly taken care of in the Roos-M\o{}lmer scheme, it appears that also decoherence due to inhomogeneous broadening on the hyperfine transition is largely suppressed.
Solid state quantum computer hardware may be based on rare-earth-ion-doped crystals. The qubits can be encoded as nuclear spin states of an ensemble of, e.g., Pr3+ ions, randomly doped into a Y2SiO5 crystal. Two such qubits can control each other through the dipole blockade effect, and transfers between the two qubit states can be done at a high fidelity, despite the strongly inhomogeneous nature of the ensemble approach. In this paper full control over the qubit Bloch sphere is demonstrated, by performing arbitrary qubit rotations and characterizing the outcomes using quantum state tomography.
We report on the implementation of quantum state tomography for an ensemble of Eu3+{\text{Eu}}^{3+}Eu3+ dopant ions in a Y2SiO5{\mathrm{Y}}_{2}{\text{SiO}}_{5}Y2​SiO5​ 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>90%>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.
We report on the implementation of quantum state tomography for an ensemble of Eu3+^{3+}3+ dopant ions in a Y2_22​SiO5_55​ crystal. The tomography was applied to a qubit based on one of the ion's 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>90>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 multi-qubit quantum computation using this system is discussed.
We experimentally demonstrate that decoherent errors for a qubit can be reduced using dynamic decoupling control. The quantum system in our experiment is a praseodymium ground-state hyperfine transition in Pr3+:Y2SiO5{\text{Pr}}^{3+}:{\text{Y}}_{2}{\text{SiO}}_{5}Pr3+:Y2​SiO5​. These experiments were undertaken using an ensemble, where care was taken to reduce incoherent errors resulting from inhomogeneity across the sample. The volume of the Bloch sphere after transformation by the applied pulse sequence was used as a measure of fidelity of the qubit. The strength of the qubit-environment coupling can be tuned by the application of a magnetic field, allowing for regimes of varying decoherence rates to be investigated. We show that the Bloch sphere volume, with the application of dynamic decoupling pulse sequences, decays at a slower rate than observed under free evolution.
We present an example of quantum process tomography (QPT) performed on a single solid-state qubit. The qubit used is two energy levels of the triplet state in the nitrogen vacancy defect in diamond. QPT is applied to a qubit which has been allowed to decohere for three different time periods. In each case, the process is found in terms of the χ matrix representation and the affine map representation. The discrepancy between experimentally estimated process and the closest physically valid process is noted. The results of QPT performed after three different decoherence times are used to find the error generators, or Lindblad operators, for the system, using the technique introduced by Boulant et al (2003 Phys. Rev. A 67 042322).