Papers › A diagrammatic method to compute the effective Hamiltonian of driven nonlinear oscillators
A diagrammatic method to compute the effective Hamiltonian of driven nonlinear oscillators
Xu Xiao, Jayameenakshi Venkatraman, Rodrigo G. Cortiñas, Shoumik Chowdhury, Michel H. Devoret
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
In this work, we present a new diagrammatic method for computing the effective Hamiltonian of driven nonlinear oscillators. At the heart of our method is a self-consistent perturbation expansion developed in phase space, which establishes a direct correspondence between the diagram and algebra. Each diagram corresponds to a Hamiltonian term, the prefactor of which, like those in Feynman diagrams, involves a simple counting of topologically equivalent diagrams. Leveraging the algorithmic simplicity of our diagrammatic method, we provide a readily available computer program that generates the effective Hamiltonian to arbitrary order. We show the consistency of our schemes with existing perturbation methods such as the Schrieffer-Wolff method. Furthermore, we recover the classical harmonic balance scheme from our result in the limit of ħ→0. Our method contributes to the understanding of dynamic control within quantum systems and achieves precision essential for advancing future quantum information processors. To demonstrate its value and versatility, we analyze five examples from the field of superconducting circuits. These include an experimental proposal for the Hamiltonian stabilization of a three-legged Schr\"odinger cat, modeling of energy renormalization phenomena in superconducting circuits experiments, a comprehensive characterization of multiphoton resonances in a driven transmon, a proposal for an inductively shunted transmon circuit, and a characterization of classical ultra-subharmonic bifurcation in driven oscillators. Lastly, we benchmark the performance of our method by comparing it with experimental data and exact Floquet numerical diagonalization.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections