Subspace Confinement: How good is your qubit?

The basic operating element of standard quantum computation is the qubit, an isolated two-level system that can be accurately controlled, initialized and measured. However, the majority of proposed physical architectures for quantum computation are built from systems that contain much more complicated Hilbert space structures. Hence, defining a qubit requires the identification of an appropriate controllable two-dimensional sub-system. This prompts the obvious question of how well a qubit, thus defined, is confined to this subspace, and whether we can experimentally quantify the potential leakage into to states outside the qubit subspace. In this paper we demonstrate that subspace leakage can be quantitatively characterized using minimal theoretical assumptions by examining the Fourier spectrum of the Rabi oscillation experiment.