# Quantum signatures of chaos, thermalization and tunneling in the exactly solvable few body kicked top

## TL;DR

This paper presents exact solutions for few-qubit quantum kicked tops, revealing quantum chaos signatures, ergodicity, and thermalization, with analytical and experimental comparisons, and explores the transition to classical behavior in larger systems.

## Contribution

It provides the first exact solutions for 3 and 4-qubit quantum kicked tops demonstrating chaos signatures and thermalization, bridging quantum and classical dynamics.

## Key findings

- Exact solutions for 3 and 4-qubit systems showing chaos signatures.
- Agreement between long-time averages and random state ensembles.
- Observation of tunneling precursor and classical bifurcation signatures.

## Abstract

Exactly solvable models that exhibit quantum signatures of classical chaos are both rare as well as important - more so in view of the fact that the mechanisms for ergodic behavior and thermalization in isolated quantum systems and its connections to non-integrability are under active investigation. In this work, we study quantum systems of few qubits collectively modeled as a kicked top, a textbook example of quantum chaos. In particular, we show that the 3 and 4 qubit cases are exactly solvable and yet, interestingly, can display signatures of ergodicity and thermalization. Deriving analytical expressions for entanglement entropy and concurrence, we see agreement in certain parameter regimes between long-time average values and ensemble averages of random states with permutation symmetry. Comparing with results using the data of a recent transmons based experiment realizing the 3-qubit case, we find agreement for short times, including a peculiar step-like behaviour in correlations of some states. In the case of 4-qubits we point to a precursor of dynamical tunneling between what in the classical limit would be two stable islands. Numerical results for larger number of qubits show the emergence of the classical limit including signatures of a bifurcation.