Hybrid Filtering for a Class of Nonlinear Quantum Systems Subject to Classical Stochastic Disturbances

Area of Science:

• Quantum physics
• Quantum information science
• Classical and quantum systems interaction

Background:

• Investigating hybrid quantum-classical systems is crucial for understanding complex dynamics.
• Classical stochastic processes can significantly impact delicate qubit systems.

Purpose of the Study:

• To develop a novel filtering strategy for hybrid quantum-classical systems.
• To model classical stochastic disturbances using an optical cavity analog.
• To obtain accurate state estimations for both cavity and classical signals.

Main Methods:

• Modeling classical disturbances with an optical cavity.
• Deriving the dynamics of the enlarged qubit-cavity quantum network.
• Formulating a stochastic master equation for the hybrid system.
• Employing the quantum-extended Kalman filter for efficient computation.

Main Results:

• Established relations between classical disturbances and the cavity analog system.
• Derived the dynamics of the integrated qubit-cavity system.
• Obtained state estimates for the cavity system and the classical signal.
• Demonstrated the effectiveness of the proposed filtering method through numerical results.

Conclusions:

• The developed quantum-classical filtering approach effectively handles disturbances in qubit systems.
• The optical cavity analog provides a viable method for modeling classical stochastic processes.
• The quantum-extended Kalman filter offers an efficient computational tool for such hybrid systems.