From classical chaotic systems to quantum qubits and qutrits

Xu Zhang; Guanrong Chen

doi:10.1063/5.0301939

From classical chaotic systems to quantum qubits and qutrits

Xu Zhang^*
, Guanrong Chen

^*Corresponding author for this work

Department of Electrical Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

1 Citation (Scopus)

Abstract

In this article, a quantum analogue of a classical chaotic system is constructed, using the Chen system and a generalized Lorenz system as an example. It is shown that if a classical system in R³ has a chaotic attractor, then a corresponding quantized system can be obtained by the density matrix theory in quantum mechanics. Furthermore, a direct transformation can be used to ensure that the basin of attraction contains the unit Bloch ball with the attractor located in its interior. As an application, a natural model for the Chen qubit is constructed and then extended to the generalized Lorenz qubit. Moreover, the Chen qutrit model is established. © 2025 Author(s). Published under an exclusive license by AIP Publishing.

Original language	English
Article number	111102
Number of pages	9
Journal	Chaos
Volume	35
Issue number	11
Online published	3 Nov 2025
DOIs	https://doi.org/10.1063/5.0301939
Publication status	Published - Nov 2025

Funding

This work was supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. T2293773 and T2293770).

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COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Xu Zhang, Guanrong Chen; From classical chaotic systems to quantum qubits and qutrits. Chaos 1 November 2025; 35 (11): 111102 and may be found at https://doi.org/10.1063/5.0301939.

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abstract = "In this article, a quantum analogue of a classical chaotic system is constructed, using the Chen system and a generalized Lorenz system as an example. It is shown that if a classical system in R3 has a chaotic attractor, then a corresponding quantized system can be obtained by the density matrix theory in quantum mechanics. Furthermore, a direct transformation can be used to ensure that the basin of attraction contains the unit Bloch ball with the attractor located in its interior. As an application, a natural model for the Chen qubit is constructed and then extended to the generalized Lorenz qubit. Moreover, the Chen qutrit model is established. {\textcopyright} 2025 Author(s). Published under an exclusive license by AIP Publishing.",

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N2 - In this article, a quantum analogue of a classical chaotic system is constructed, using the Chen system and a generalized Lorenz system as an example. It is shown that if a classical system in R3 has a chaotic attractor, then a corresponding quantized system can be obtained by the density matrix theory in quantum mechanics. Furthermore, a direct transformation can be used to ensure that the basin of attraction contains the unit Bloch ball with the attractor located in its interior. As an application, a natural model for the Chen qubit is constructed and then extended to the generalized Lorenz qubit. Moreover, the Chen qutrit model is established. © 2025 Author(s). Published under an exclusive license by AIP Publishing.

AB - In this article, a quantum analogue of a classical chaotic system is constructed, using the Chen system and a generalized Lorenz system as an example. It is shown that if a classical system in R3 has a chaotic attractor, then a corresponding quantized system can be obtained by the density matrix theory in quantum mechanics. Furthermore, a direct transformation can be used to ensure that the basin of attraction contains the unit Bloch ball with the attractor located in its interior. As an application, a natural model for the Chen qubit is constructed and then extended to the generalized Lorenz qubit. Moreover, the Chen qutrit model is established. © 2025 Author(s). Published under an exclusive license by AIP Publishing.

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VL - 35

JO - Chaos

JF - Chaos

IS - 11

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ER -

From classical chaotic systems to quantum qubits and qutrits

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