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Chaos, Fractals, and Ergodicity in Nonlinear Quantum Protocols

  • Attila Portik
  • Orsolya Kálmán
  • Tamás Kiss
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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.

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Cite

BibTeXRIS
BibTeX
@misc{portik2026chaos,
  title = {{Chaos, Fractals, and Ergodicity in Nonlinear Quantum Protocols}},
  author = {Attila Portik and Orsolya Kálmán and Tamás Kiss},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01249},
  eprint = {2611.01249},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01249},
}
RIS
TY  - UNPB
TI  - Chaos, Fractals, and Ergodicity in Nonlinear Quantum Protocols
AU  - Attila Portik
AU  - Orsolya Kálmán
AU  - Tamás Kiss
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01249
UR  - https://arxiv.org/abs/2611.01249
AB  - 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.
ER  -