Exposing Hypersensitivity in Quantum Chaotic Dynamics

TL;DR

This paper reveals that multi-qubit quantum systems can exhibit hypersensitivity to initial states, challenging classical chaos detection methods, and shows that a quantum state-metric effectively identifies quantum chaos.

Contribution

It introduces the use of a quantum state-metric to detect hypersensitivity and chaos in multi-qubit quantum systems, bridging classical and quantum chaos signatures.

Findings

Hypersensitivity correlates with quantum chaos signatures

Quantum state-metric detects chaos in the same regimes as classical systems

Multi-qubit quantum kicked top exhibits hypersensitivity similar to classical chaos

Abstract

We demonstrate that the unitary dynamics of a multi-qubit system can display hypersensitivity to initial state perturbation. This contradicts the common belief that the classical approach based on the exponential divergence of initially neighboring trajectories cannot be applied to identify chaos in quantum systems. To observe hypersensitivity we use quantum state-metric, introduced by Girolami and Anza in [Phys. Rev. Lett. 126 (2021) 170502], which can be interpreted as a quantum Hamming distance. As an example of a quantum system, we take the multi-qubit implementation of the quantum kicked top, a paradigmatic system known to exhibit quantum chaotic behavior. Our findings confirm that the observed hypersensitivity corresponds to commonly used signatures of quantum chaos. Furthermore, we demonstrate that the proposed metric can detect quantum chaos in the same regime and under analogous initial conditions as in the corresponding classical case.