Transmon qudit control and tomography via multi-frequency driving

Qudits hold great promise for efficient quantum computation and the simulation of high-dimensional quantum systems. Most qudit experiments to date have relied on decompositions of SU(d) operations into series of qubit-like rotations between two-level subspaces of adjacent states. In this talk I will discuss recent experiments which employed simultaneous multi-frequency drives to generate rotations in an effective spin-7/2 system mapped onto the energy eigenstates of a superconducting circuit. We implement single-shot readout of the 8 states using multi-tone dispersive readout and exploit the strong nonlinearity in a high-EJ/EC transmon to simultaneously address each transition and realize a spin displacement operator. Combining the displacement operator with a virtual SNAP gate, we realize arbitrary single-qudit unitary operations in O(d) physical pulses. We extend this to a new scheme for qudit state tomography requiring only O(d) pulses to fully characterize a qudit state. Our approach to qudit control and measurement can be readily extended to other physical platforms that realize a multi-level system coupled to a cavity and can become a building block for efficient qudit-based quantum computation and simulation.