Universal sideband control of a qudit encoded in an oscillator

Universal control of an oscillator has been demonstrated using gate sets based on oscillator displacements combined with selective number arbitrary phase (SNAP) gates [1] or echoed conditional displacements (ECD) and qubit rotations [2]. Sideband interactions, which exchange photons between a qubit and cavity, have been used to implement state preparation as well as a class of unitary encoding gates [3], though universal control has not yet been demonstrated. We present a new method for universal oscillator control that decomposes unitary gates into discrete sideband and qubit rotations, where the qubit is realized in the ground (g) and second-excited (f) states of a transmon and the oscillator in a microwave cavity mode. We construct our gate set so that operations are closed below a chosen oscillator cutoff dimension, thereby defining a qudit in the oscillator and suppressing leakage outside the control subspace. Our protocol is constructed so that transmon decay events send the state into the first-excited (e) manifold, allowing these errors to be heralded. We explore how unitaries implemented with our control technique scale with qudit dimension and present experimental implementations of qudit gates in an oscillator.

[1] Heeres, R. et al. Phys. Rev. Lett. 115, 137002 (2015)

[2] Eickbusch, A. et al. Nat. Phys. 18, 1464–1469 (2022)

[3] Huang, J. et al. arXiv:2503.10623 (2025)