  Single-step implementations of multi-qubit gates are generally believed to
provide a simpler design, a faster operation, and a lower decoherence. For
coupled three qubits interacting with a photon field, a realizable scheme for a
single-step Toffoli gate is investigated. We find that the three qubit system
can be described by four effective modified Jaynes-Cummings models in the
states of two control qubits. Within the rotating wave approximation, the
modified Jaynes-Cummings models are shown to be reduced to the conventional
Jaynes-Cummings models with renormalized couplings between qubits and photon
fields. A single-step Toffoli gate is shown to be realizable with tuning the
four characteristic oscillation periods that satisfy a commensurate condition.
Possible values of system parameters are estimated for single-step Toffli gate.
From numerical calculation, further, our single-step Toffoli gate operation
errors are discussed due to imperfections in system parameters, which shows
that a Toffoli gate with high fidelity can be obtained by adjusting pairs of
the photon-qubit and the qubit-qubit coupling strengthes. In addition, a
decoherence effect on the Toffoli gate operation is discussed due to a thermal
reservoir.
