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Among the many proposals for the realization of a quantum computer, holonomicquantum computation (HQC) is distinguished from the rest in that it isgeometrical in nature and thus expected to be robust against decoherence. Herewe analyze the realization of various quantum gates by solving the inverseproblem: Given a unitary matrix, we develop a formalism by which we find loopsin the parameter space generating this matrix as a holonomy. We demonstrate forthe first time that such a one-qubit gate as the Hadamard gate and suchtwo-qubit gates as the CNOT gate, the SWAP gate and the discrete Fouriertransformation can be obtained with a single loop.Comment: 8 pages, 6 figure

Realization of arbitrary gates in holonomic quantum computation