Jordan’s paper on Universal Jaynes-Cummings Control of an Oscillator, with Ethan Kasaba, Thomas DiNapoli and Tanay Roy, is now on the arXiv.
The Jaynes-Cummings interaction is the most basic coupling between a two level system and an oscillator, and it is native to trapped ions, mechanical resonators and magnonic systems as well as to superconducting circuits. Until now it had been used mainly for state preparation and for a restricted set of gates. We show that it is enough on its own: any unitary on a chosen d dimensional Fock subspace can be compiled into an alternating sequence of ancilla rotations and Jaynes-Cummings interactions.
The key is that each Jaynes-Cummings layer performs a full 2π rotation on the cutoff transition. The dynamics then close inside the computational subspace, so the gate set is leakage protected by construction, and ancilla relaxation events become detectable at the end of any sequence and can be removed by post-selection. We measured a complete universal qutrit gate set with a mean post-selected process fidelity of 96%, along with ququart and ququint shift gates at 95% and 94%.
Circuit depth grows as d2, and is remarkably similar for Clifford gates, non-Clifford gates and Haar random unitaries. The gate time grows more slowly, as d3/2, because the √n bosonic enhancement of the Jaynes-Cummings rate speeds up every layer. The dispersive shift, which would normally degrade performance, instead serves as a compilation resource that shortens circuits once the sideband drive detuning is used as an additional control knob.
Compiling arbitrary qudit unitaries from Jaynes-Cummings interactions. Top left: each layer drives a 2π rotation on the cutoff transition, closing the dynamics within the computational subspace. Top right: measured process fidelities for the universal qutrit gate set. Bottom: measured Wigner functions of the oscillator before and after a compiled gate.
Read the preprint at arXiv:2605.18658, or see the short summary on our Highlights page.