Quantum Fourier transform of polarization photons mediated by weak cross-Kerr nonlinearity

We present a scheme of two-photon quantum Fourier transform at first, where the controlled π/2 phase gate and the Hadamard gates are applied. The indirect interaction between two photons can be realized through a coupling bus provided by a coherent state in Kerr media. Employing photon-number measurements and the corresponding classical feed-forward techniques, the task of low-error quantum Fourier transform can be fulfilled. With revision and modulation on the optical elements, controlled π/2n (n=2,3,…) phase gates are constructed, and the multiphoton quantum Fourier transform can be achieved by integrating these controlled phase gates and Hadamard gates.

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