Creating Qubit States with Degenerate Two-level Systems

A qubit, or quantum bit, is conventionally defined as "a physical system for storing information that is capable of existing in either of two quantum states or in a superposition of both". In this paper, we examine the simple question of whether two distinct levels, each consisting of multiply degenerate sub-states, could serve as a practical quantum bit. We explore this idea using a well-characterized atomic system of the kind employed in several quantum computing implementations. We approximate the atom as a two-level system without degeneracy lifting in the magnetic quantum number while using the angular momentum addition rules to select the desired state transition. We find that, in the continuous presence of the field, the atom still undergoes Rabi oscillations, which are suitable for quantum gate construction. In addition, we compute the average fidelity in quantum gate performance for a single degenerate atom and postulate the required form of two-atom interaction to construct a controlled Z gate.