Emulating 2 qubits with a 4-level superconducting transmon

Near-term quantum algorithms for quantum chemistry require the quantum device to provide a sufficiently large Hilbert space to encode the chemistry target. Traditionally such a large Hilbert space is achieved with many two-level systems. Utilizing additional levels of the quantum system would be beneficial in reducing hardware complexity. Here we present a variational quantum eigensolver using four levels of a superconducting transmon device. We use this 4-level system to emulate a two-qubit system and demonstrate solving hydrogen molecule eigenstates.