Quantum Chaos Systems and Fidelity

P. Lebœuf

Joseph Emerson, Yaakov S. Weinstein, Seth Lloyd +1 more

We demonstrate that a system's rate of fidelity decay under repeated perturbations may be measured efficiently on a quantum information processor, and analyze the conditions under which this indicator is a reliable probe of quantum chaos. The type and rate of the decay are not dependent on the eigenvalue statistics of the unperturbed system, but depend on the system's eigenvector statistics in the eigenbasis of the perturbation. For random eigenvector statistics, the decay is exponential with a rate fixed by the variance of the perturbation's energy spectrum. Hence, even classically regular models can exhibit an exponential fidelity decay under generic quantum perturbations. These results clarify which perturbations can distinguish classically regular and chaotic quantum systems.

Jincheng Zhang

This paper presents the design and preliminary verification of a quantum chaos simulator. The core concept involves leveraging quantum phenomena, specifically superposition and interference, to emulate the behavior of classical chaotic systems. Traditional classical chaos simulators are fundamentally limited by the constraints of classical computation, often struggling with the inherent numerical inaccuracies and computational demands associated with simulating chaotic dynamics. Conversely, a quantum chaos simulator offers the potential to overcome these limitations. By harnessing the principles of quantum mechanics, this design proposes a controlled quantum system capable of accurately simulating complex chaotic systems and, potentially, exploring novel quantum chaotic phenomena. The design focuses on a specific architecture and key control parameters, outlining a pathway toward demonstrable simulation fidelity. This work establishes a foundational approach for future research and development in the field of quantum chaos simulation.

W. D. Heiss

Tyler LeBlond, Dries Sels, Anatoli Polkovnikov +1 more

We show that the onset of quantum chaos at infinite temperature in two many-body one-dimensional lattice models, the perturbed spin-1/2 XXZ and Anderson models, is characterized by universal behavior. Specifically, we show that the onset of quantum chaos is marked by maxima of the typical fidelity susceptibilities that scale with the square of the inverse average level spacing, saturating their upper bound, and that the strength of the integrability- or localization-breaking perturbation at these maxima decreases with increasing system size. We also show that the spectral function below the ``Thouless'' energy (in the quantum-chaotic regime) diverges when approaching those maxima. Our results suggest that, in the thermodynamic limit, arbitrarily small integrability- or localization-breaking perturbations result in quantum chaos in the many-body quantum systems studied here.

G. P. Berman