Universal Jaynes-Cummings Control of an Oscillator

TL;DR

This paper demonstrates universal control of a quantum harmonic oscillator using Jaynes-Cummings interactions and qubit rotations, enabling programmable bosonic processors across various quantum platforms.

Contribution

The authors develop and experimentally realize a method for universal oscillator control via JC interactions, including high-fidelity qudit gates and error suppression techniques.

Findings

Achieved a mean post-selected process fidelity of 96% for a single-qutrit gate.

Demonstrated control over ququarts and ququints using JC interactions.

Implemented a universal gate set for oscillator control with suppressed leakage errors.

Abstract

The Jaynes-Cummings (JC) interaction-the coherent exchange of excitations between a two-level system and a harmonic oscillator-is one of the fundamental interactions of quantum optics, realized across platforms such as cavity quantum electrodynamics, trapped ions, mechanical resonators, and superconducting circuits. Although JC interactions and qubit rotations form a universal gate set for oscillator control, practical implementations have not been demonstrated. Here we develop and experimentally demonstrate universal JC-based oscillator control by compiling arbitrary unitary gates into sequences of JC interactions and qubit rotations. In our experiment, the oscillator is realized using a mode of a high quality factor microwave cavity and the ancilla qubit using a superconducting transmon circuit, with the JC interaction implemented by a sideband interaction enabled by the Josephson nonlinearity. The native gates are constructed to be closed below a chosen cutoff photon number, encoding a qudit with suppressed leakage errors, while ancilla relaxation errors are detectable. We further find that the dispersive shift serves as a compilation resource that reduces circuit depths. We demonstrate universal qudit control and implement a single-qutrit gate set with a mean post-selected process fidelity of 96%, as well as ququart and ququint shift gates. These results establish Jaynes-Cummings control as a practical route to universal oscillator control, enabling programmable bosonic processors across a variety of quantum platforms.