  Quantum bits, or qubits, are the fundamental building blocks of present
quantum computers. Hence, it is important to be able to characterize the state
of a qubit as accurately as possible. By evaluating the qubit characterization
problem from the viewpoint of quantum metrology, we are able to find optimal
measurements under the assumption of good prior knowledge. We implement these
measurements on a superconducting quantum computer. Our experiment produces
sufficiently low error to allow the saturation of the theoretical limits, given
by the Nagaoka--Hayashi bound. We also present simulations of adaptive
measurement schemes utilizing the proposed method. The results of the
simulations show the robustness of the method in characterizing arbitrary qubit
states with different amounts of prior knowledge.
