Abstract
A scheme is proposed for realizing geometric quantum computation with one-qubit unitary gates and $N$-qubit $(N\ensuremath{\ge}2)$ phase gates in cavity QED. In the scheme, the cavity field and excited states are virtually excited by controlling appropriately atom-field couplings and engineering adiabatic passage; thus the gate operations are insensitive to the cavity decay and the atomic spontaneous emission. Furthermore, the $N$-qubit $(N\ensuremath{\ge}2)$ geometric phase gates can be realized just by one step and the required time does not increase with the number of qubits, which can significantly reduce complexity of physical realization of practical quantum computation and quantum algorithms.
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