  We propose a scheme to perform basic gates of quantum computing and prepare
entangled states in a system with cold trapped ions located in a single mode
optical cavity. General quantum computing can be made with both motional state
of the trapped ion and cavity state being qubits. We can also generate
different kinds of entangled states in such a system without state reduction,
and can transfer quantum states from the ion in one trap to the ion in another
trap. Experimental requirement for achieving our scheme is discussed.
