Efficient Control of a Transmon Qudit Using Effective Spin- 7/2 Rotations

Abstract

Qudits hold great promise for efficient quantum computation and the simulation of high-dimensional quantum systems [1]. However, existing control and measurement schemes for qudit systems scale unfavorably with qudit dimension since they decompose SU(d) operations into series of qubitlike rotations and perform measurements on a small number of states [2-6]. Here, we address these challenges by employing simultaneous multifrequency drives to generate rotations and projections in an effective spin-7/2 system mapped onto the energy eigenstates of a superconducting circuit. We implement single-shot readout of the eight states using a multitone dispersive readout (Fassignment=88.3%) and exploit the strong nonlinearity in a high-EJ/EC transmon to simultaneously address each transition and realize a spin displacement operator. Combining this displacement operator with a virtual SNAP gate, we realize arbitrary single-qudit unitary operations in O(d) physical pulses and extract spin displacement gate fidelities ranging from 0.997 to 0.989 for virtual spins of size j=1 to j=7/2. We demonstrate the potential of our control scheme in three ways: the direct measurement of the spin qudit Wigner function, randomized benchmarking of a logical qubit encoded into the qudit state, and randomized benchmarking of the full qudit Clifford group. In the latter experiment, we implement the d-dimensional quantum Fourier transform with an average gate fidelity of 0.91(6) in d=8. Our multifrequency approach to qudit control and measurement can be readily extended to other physical platforms that realize a multilevel system coupled to a cavity and can become a building block for efficient qudit-based quantum computation and simulation.