Qudit Encodings in Superconducting Circuits: Taking the Transmon for a Spin

Encoding of quantum information in many-level systems provides a resource efficient path towards quantum computing-, and simulation. Here we explore the excited states of transmons with E_J/E_C up to 325. We demonstrate preparation and readout of Fock states of up to eleven microwave photons [1] and efficient qudit control using spin-displacement operations that correspond to rotations of large-angular moment spins [2]. The ability to readout and control a high-dimensional transmon qudit provides a unique way to study Josephson Harmonics, transmon decoherence, and measurement-induced state transitions. In the long term, we anticipate this new approach to controlling higher-level quantum information to yield benefits for bosonic quantum error correction and qu-dit simulation.