  The current proposals for the realization of quantum computer such as NMR,
quantum dots and trapped ions are based on the using of an atom or an ion as
one qubit. In these proposals a quantum computer consists from several atoms
and the coupling between them provides the coupling between qubits necessary
for a quantum gate. We discuss whether a {\it single} atom can be used as a
quantum computer. Internal states of the atom serve to hold the quantum
information and the spin-orbit and spin-spin interaction provides the coupling
between qubits in the atomic quantum computer. In particular one can use the
electron spin resonance (ESR) to process the information encoded in the
hyperfine splitting of atomic energy levels. By using quantum state engineering
one can manipulate the internal states of the natural or artificial (quantum
dot) atom to make quantum computations.
