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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Solid state qubit quantum state tomography

Andreas Walther, Lars Rippe, Brian Julsgaard, Stefan Kröll

Published Jan 22, 2008• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.772312

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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.
An overview of current status and prospects of the development of quantum computer hardware based on inorganic crystals doped with rare-earth ions are presented. Major parts of the experimental work in this area have been done in two places, Canberra, Australia and Lund, Sweden, and the present description follows more closely the Lund work. Techniques will be described that include optimal filtering of the initially inhomogeneously broadened profile down to well separated and narrow ensembles, as well as the use of advanced pulse-shaping in order to achieve robust arbitrary single-qubit operations with fidelities above 90%, as characterized by quantum state tomography. It is expected that full scalability of these systems will require the ability to determine the state of single rare-earth ions. It has been proposed that this can be done using special readout ions doped into the crystal and an update is given on the work to find and characterize such ions. Finally, a few aspects on possibilities for remote entanglement of ions in separate rare-earth-ion-doped crystals are considered.
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.
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.
Rare-earth ions doped into a transparent crystal can have optically excited states with coherence times of milliseconds and hyperfine levels with coherence times of hours when cooled down to liquid helium temperatures. This makes them attractive for developing quantum computing hardware. A quantum transistor can be implemented in a rare-earth-ion-doped crystal by utilizing a dipole blockade effect, where one excited ion prevents nearby ions from being excited. By using single rare-earth ions as qubits, the quantum processor is believed to be scalable to several qubits. In this thesis a readout mechanism for qubits represented by single ions (Eu or Pr) in a Y2SiO5 crystal is explored. A single cerium ion, in the same crystal as the qubits, could potentially be used as an indicator ion for non-demolition quantum state detection of the qubits. Cerium has a strong transition with high fluorescence yield which makes it possible to detect single ions. A cerium ion can be controlled by a qubit via the dipole blockade effect, and fluoresce if the qubit is in state |1> but stay dark if the qubit is in state |0>. Relevant spectroscopic properties of Ce:Y2SiO5 are studied, as well as interactions between cerium ions and qubit ions. The inhomogeneous and homogeneous linewidth of the Ce:Y2SiO5 4f-5d transition is measured and fluorescence spectra for ions in site 1 and site 2 are characterized. The change in electric dipole moment as a cerium ion is brought to the excited state is measured. The static dipole interaction between a single cerium ion and a qubit ion is shown to be strong enough for efficient qubit readout. Energy transfer from cerium to qubit ions is investigated. A lower bound on the cerium-qubit distance is found in order to avoid energy transfer. Satellite lines belonging to cerium-qubit pairs are mapped out. A microscope set-up is built to detect single ions in a crystal. Single ion detection is believed to be within reach.
We present a scheme for quantum computing in rare-earth-ion doped inorganic crystals. We use two of the ground state hyperfine levels as the qubit states, with different qubits absorbing light at different frequencies within an inhomogeneously broadened optical transition. Interaction between different qubits is accomplished using the change in permanent dipole moment that is induced at the optical excitation of the ions. The two most important aspects of the scheme have been accomplished experimentally: The isolation of a single qubit in a pure state and interaction between ions absorbing at different frequencies.