The Use of Hilbert-Schmidt Decomposition for Implementing Quantum Gates

It is shown how to realize quantum gates by decomposing the gates into summation of unitary matrices where each of these matrices is given by a tensor multiplication of the unit and Pauli 2x2 spin matrices. It is assumed that each of these matrices is operating on a different copy of the quantum states produced by 'quantum encoders' with a certain probability of success. The use of the present probabilistic linear optics' method for realizing quantum gates is demonstrated by the full analysis given for the control phase shift gate, but the use of the present method for other gates, including the control-not gate, is also discussed.

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