02 (2010 Selected)：⇒This research proposal was terminated at the end of March 2011 due to be selected by Funding Program for Next Generation World-Leading Researchers (NEXT Program).

Realization of cluster quantum computation using a Fermi-degenerate ¹⁷¹Yb atomic ensemble

The objective of this study is to realize cluster quantum computation by applying cavity QED technology to a Fermi-degenerate ¹⁷¹Yb atomic ensemble. In 2001, cluster quantum computation was proposed by Raussendorf and Briegel [1]. Unlike conventional quantum computation by a combination of unitary gates, in cluster quantum computation the cluster state is generated among a number of qubits and the projective measurement of each qubit is then performed. Cluster computation is invaluable for systems, such as neutral atomic gases, where a very large number of qubits (as many as 10⁶) are relatively readily available and can be regularly arranged by optical lattices. In 2003, Bloch et al. succeeded in generating a cluster state. They caused the Mott transition of Rb condensates, individually trapped atoms in optical lattice sites, and then performed electron-dependent potential control to induce an Ising-type interaction, creating a cluster state [2]. This success significantly increased the possibility of realizing large-scale quantum computation. Unfortunately, however, due to the use of electron spins, the coherence time was as short as 1 ms. In addition, the projective measurement of individual electron spin was not possible.

In this publicly solicited research project, we aim to realize cluster quantum computation based on the following five principles:

1. Use as a qubit a nuclear spin with a coherence time 2000 times that of an electron spin. Specifically, 1/2 the nuclear spin of the ground state of ¹⁷¹Yb is used.

2. Arrange Yb atomic ensembles as qubits in arrays in a plane of about 1 μm on the object lens surface. Make it possible to examine in detail the arrangement of qubits by high-resolution fluorescence microscopy using the solid immersion effect.

3. Generate a cluster state required for computation using a new mechanism called a nuclear spin-dependent optical trap based on forbidden transitions normally used only in atomic clocks. Realize the real-time operation of potential using a spatial phase modulator.

4. The key to the success of cluster computation is whether the projective measurement of individual spins can be performed with high quantum efficiency. Realize high-speed, high-efficiency projective measurement using cavity QED technology based on optical microcavities. For its realization, the fluorescence emission rate is increased for microsecond-scale observation by exciting specific atoms in an optical lattice to the ³P² metastable state and applying cavity QED using an allowed transition from the ³P² metastable state to the ³D³ state.

In our previous studies, we have measured the quantum state of the nuclear spins of a single Yb atom and developed techniques for full control of the quantum state. These include projective measurement of a single nuclear spin using a bias magnetic field [3]; measurement intensity control using a single photon as an ancilla [4]; trapping of a single Yb atom for a few seconds in an optical microcavity, as well as quantum tomography with a fidelity of more than 0.98 [5]; and projective measurement of a single nuclear spin by two-mode cavity QED [6]. Using these techniques, we aim to realize cluster quantum computation using Yb atoms in a two-dimensional optical lattice.

[1] R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001).
[2] O. Mandel et al., Nature (London) 425, 937 (2003).
[3] M. Takeuchi et al., Phys. Rev. A 81, 062308 (2010).
[4] N. Takei et al., Phys. Rev. A 81, 042331 (2010).
[5] A. Noguchi et al., arXiv: 1005.3584 (2010).
[6] Y. Eto et al., arXiv: 1012.1724 (2010).

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