Chaos, Fractals, and Ergodicity in Nonlinear Quantum Protocols

Abstract:Iterated nonlinear quantum protocols provide a straightforward way of realizing nonlinear dynamics in quantum systems through measurement and postselection. We investigate a family of protocols in which the order of the induced nonlinearity is controlled by the number of qubits involved in a single step. By examining the resulting rational maps and applying a set of numerical diagnostics, we identify extended parameter regions that exhibit ergodic-like dynamics for protocol orders $n=3,4,$ and $5$. We further characterize the associated chaotic behavior through the distribution of Lyapunov exponents. Our results show that ergodic-like dynamics persists beyond the quadratic case, while the geometry of the corresponding parameter regions and the typical degree of chaoticity depend strongly on the order of the nonlinear transformation.

Quantum Physics (quant-ph); Chaotic Dynamics (nlin.CD)

arXiv:2611.01249 [quant-ph]

(or arXiv:2611.01249v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2611.01249 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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