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From classical chaotic systems to quantum qubits and qutrits.

Xu Zhang1, Guanrong Chen2

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This study constructs quantum chaotic systems from classical ones like the Chen system. These quantum systems, utilizing density matrix theory, can be applied to create novel quantum bits (qubits) and qutrits.

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Area of Science:

  • Quantum mechanics
  • Classical chaos theory
  • Quantum information science

Background:

  • Classical chaotic systems exhibit complex dynamics.
  • Quantum mechanics offers a framework for describing systems at the atomic and subatomic levels.
  • Bridging classical chaos and quantum mechanics is crucial for developing advanced quantum technologies.

Purpose of the Study:

  • To construct a quantum analogue of classical chaotic systems.
  • To apply density matrix theory to quantize chaotic systems.
  • To develop quantum models for qubits and qutrits based on chaotic systems.

Main Methods:

  • Utilized the Chen system and a generalized Lorenz system as classical examples.
  • Employed density matrix theory from quantum mechanics for quantization.
  • Applied a direct transformation to map classical attractors to the Bloch ball.

Main Results:

  • Successfully constructed quantum analogues of classical chaotic systems.
  • Demonstrated that chaotic attractors in R3 can be quantized.
  • Developed a Chen qubit, a generalized Lorenz qubit, and a Chen qutrit model.

Conclusions:

  • The density matrix theory provides a viable method for quantizing classical chaotic systems.
  • The developed quantum models offer new possibilities for quantum computation and information processing.
  • This work establishes a foundation for exploring quantum chaos in engineered quantum systems.