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A Model for Encoding Multiple Logical Qubit States into the Energy Eigenstates of a Transmon System

One of the main challenges in implementing a Quantum Computer is the realization of two-qubit gates. In contrast to single qubit gates, for which advanced quantum controls are available for a variety of physical systems, the coupling required for two-qubit systems typically introduces more noise and poses an obstacle for arbitrary scaling of the underlying architecture. In this paper, we investigate a new model that partially overcomes the coupling problem. The model is based on encoding multiple logical states into the energy eigenstates of a single physical system, thereby allowing two qubit gates to be realized using the logical states that are spanned by the energy spectrum of the system. The work presented here expands upon previous work by the authors that was implemented and validated using tarnsmon technology in IBM's quantum experience for the two-qubit register case; here the model is expanded to demonstrate how it can encode quantum registers of arbitrary size.