A simple phase estimation procedure is outlined and applied to solve standard quantum-mechanical problems. The procedure needs only one qubit to read off the eigenenergy obtained by iterative measurements, while the system qubits provides the corresponding eigenstates. No a priori information is needed about the system states and energies, therefore, the procedure may be launched from a completely random initial state.

• Received 28 March 2008

DOI:https://doi.org/10.1103/PhysRevA.78.022337