  Conditional quantum oscillations are investigated for quantum gate operations
in superconducting flux qubits. We present an effective Hamiltonian which
describes a conditional quantum oscillation in two-qubit systems. Rabi-type
quantum oscillations are discussed in implementing conditional quantum
oscillations to quantum gate operations. Two conditional quantum oscillations
depending on the states of control qubit can be synchronized to perform
controlled-gate operations by varying system parameters. It is shown that the
conditional quantum oscillations with their frequency synchronization make it
possible to operate the controlled-NOT and -U gates with a very accurate gate
performance rate in interacting qubit systems. Further, this scheme can be
applicable to realize a controlled multi-qubit operation in various solid-state
qubit systems.
