Implementation of selective quantum gates in a neutral atom quantum computer

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A system of neutral atoms trapped in a lattice form by using Fresnel traps are considered. The qubit state is a vector in a vector space spanned by two hyperfine states. By further introducing a one-dimensional optical lattice, it is possible to act a two-qubit quantum gate on an arbitrary pair of two atoms, which may be far apart. In the proposed method, the radius of the shutter producing the Fresnel trap must be variable. If, however, the pair of atoms on which the gate acts is restricted to a nearest neighbor atoms, it is possible to act a two-qubit gate without varying the radius of the shutter. We also consider to implement composite gates, in which high-precision gates are realized by combining low-precision gates. Quantum system is vulnerable against external noise. We developed efficient quantum error correcting codes by which the noise is avoided.