Scheme for Implementing Grover Quantum Search Algorithm with Hot Ions

We propose a simple scheme to implement the two-qubit Grover quantum search algorithm with trapped ions in thermal motion. In the scheme two states of the I >-type three-level ions are used as quantum bits (qubits). The scheme puts no limitations on the intensity of the laser field and the speed of the hot ions, and all the operations can be achieved in a reasonable amount of time before decoherence sets in. The scheme might be experimentally realizable with presently available techniques.