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We demonstrate that the unitary dynamics of a multi-qubit system can displayhypersensitivity to initial state perturbation. This contradicts the commonbelief that the classical approach based on the exponential divergence ofinitially neighboring trajectories cannot be applied to identify chaos inquantum systems. To observe hypersensitivity we use quantum state-metric,introduced by Girolami and Anza in [Phys. Rev. Lett. 126 (2021) 170502], whichcan be interpreted as a quantum Hamming distance. As an example of a quantumsystem, we take the multi-qubit implementation of the quantum kicked top, aparadigmatic system known to exhibit quantum chaotic behavior. Our findingsconfirm that the observed hypersensitivity corresponds to commonly usedsignatures of quantum chaos. Furthermore, we demonstrate that the proposedmetric can detect quantum chaos in the same regime and under analogous initialconditions as in the corresponding classical case.

Exposing Hypersensitivity in Quantum Chaotic Dynamics