Fundamental Limits to Cat-Code Qubits from Chaos-Assisted Tunneling

TL;DR

This work demonstrates that chaos-assisted tunneling (CAT) imposes a fundamental limit to Kerr-cat qubits: whereas the static effective description predicts exponentially suppressed tunneling between the cat states, the driven system exhibits chaos-mediated tunneling that yields large quasi-energy splittings $\Delta E$. The authors combine Floquet theory, full quantum simulations, and semiclassical WKB estimates (with Fermi golden rule) to quantify tunneling rates and connect splittings to chaos. They provide quantitative evidence of CAT in a superconducting qubit, achieving agreement across Floquet, quantum-decay, and semiclassical methods and revealing a chaos-induced plateau in the tunneling rate. The results identify chaos as an intrinsic coherence limit for dynamically protected cat-code qubits, with broad implications for parameter choices and the fundamental interplay between nonlinear dynamics, periodic driving, and quantum fault tolerance.

Abstract

We show that chaos-assisted tunneling (CAT) imposes an intrinsic limit to the protection of Kerr-cat qubits. In the static effective description, tunneling between the quasi-degenerate cat states can be exponentially suppressed, ensuring long lifetimes. However, our Floquet analysis reveals that when the nonlinearities increase, chaotic states mediate tunneling between the cat states, producing large quasi-energy splittings. We compute tunneling rates using both full quantum simulations and semiclassical WKB theory, finding quantitative agreement and confirming that the splittings are directly linked to chaos. These results provide the first evidence of CAT in the Kerr-cat qubit and demonstrate that chaos sets a fundamental bound on the coherence of dynamically protected superconducting qubits.

Figures (4)

• Figure 1: Scaled quasi-energy split $\Delta E/K$ as a function of K, for the case $\epsilon_2/K=50$ and $\Delta/K=10$. $N=250$, $g_3=0.02$, $g_4=10^{-8}$. Solid blue line corresponds to $\Delta E/K$ computed from the time dependent Hamiltonian. The pink (almost constant $\approx 10^{-12}$) line corresponds to $\Delta E/K$ obtained for the static effective Hamiltonian. Open circles correspond to quantum calculations. Filled circles correspond to the semiclassical approximation.
• Figure 2: Visual interpretation of the CAT affecting the ground state of the Kerr parametric oscillator. The green points correspond to the classical Poincaré section. The tunneling takes place, mediated by a chaotic state with quasi-energy near that of the ground state, with a rate $\gamma$.
• Figure S1: Scaled quasi-energy $\Delta E/K$ as a function of $\rm K$, for the cases $\epsilon_2/K=10$ and $\Delta/K=0.2$ (left panel), and $\epsilon_2/K=30$ and $\Delta/K=10$ (right panel). $N=250$, $g_3=0.02$, $g_4=10^{-8}$. Solid blue lines for both panels correspond to $\Delta E/K$ computed from the time dependent Hamiltonian. The pink line corresponds to $\Delta E/K$ obtained for the static effective Hamiltonian with the dashed green line on the left panel exhibiting the splitting limit shown in venkatraman2025thesis. Open circles correspond to quantum calculation. Filled circles correspond to the semiclassical approximation.
• Figure S2: IPN (left panel) and Wehrl entropy (right panel) comparison between the effective approximation (blue line) and the Floquet-solved system (orange line). Parameters are $\Delta/K=0.2$, $\epsilon_2/K=10$, and $K=0.002$. These sets of parameters correspond to a point on the left panel of Fig. \ref{['fig:1S']}. Both quantities serve as indicators of delocalization in the coherent-state basis.