ABSTRACT: An efficient coding circuit is given for the perfect quantum-error correction of a single quantum bit (qubit) against arbitrary one-qubit errors within a five-qubit code. The circuit presented employs a double "classical" code, i.e., one for bit flips and one for phase shifts. An implementation of this coding circuit on an ion-trap quantum computer is described that requires 26 laser pulses. Another circuit is presented requiring only 24 laser pulses, making it an efficient protection scheme against arbitrary one-qubit errors. In addition, the performances of two error-correction schemes, one based on the quantum Zeno effect and the other using standard methods, are compared. The quantum Zeno error correction scheme is found to fail completely for a model of noise based on phase diffusion.