Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exhibition of the periodicity of Quantum Fourier Transformation in
  Nuclear Magnetic Resonance   The remarkable capability of quantum Fourier transformation (QFT) to extract
the periodicity of a given periodic function has been exhibited by using
nuclear magnetic resonance (NMR) techniques. Two separate sets of experiments
were performed. In a full QFT, the periodicity were validated with state
tomography and fidelity measurements. For a simplified QFT, the three-qubit
pseudo-pure state was created by introducting an additional observer spin, and
the spectra recorded on the observer spin showed intuitively the power of QFT\
to find the periodicity. Experimentally realizing the QFT provides a critical
step to implement the renowned Shor's quantum factoring algorithm and many
other algorithms. Moveover, it can be applied to the study of quantum chaos and
other quantum information processing.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: math
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The categories of this paper are: atom-ph