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Dynamic estimation of probability density using quantum neural network based on simple harmonic oscillator perturbed
Guguloth Sagar1, Harish Parthasarathy1, Vijyant Agarwal1
1Netaji Subhas University of Technology, New Delhi, India.
Cognitive Neurodynamics
|August 15, 2025
Summary
This study introduces a quantum neural network that controls a quantum harmonic oscillator
Area of Science:
- Quantum mechanics
- Computational physics
- Machine learning
Background:
- Quantum harmonic oscillators are fundamental systems in quantum mechanics.
- Controlling quantum systems is crucial for quantum computing and simulation.
- Probability density functions (PDFs) describe quantum state distributions.
Purpose of the Study:
- To propose a quantum neural network (QNN) for controlling quantum systems.
- To demonstrate the generation of time-varying wave functions in the Schrodinger equation.
- To track a target probability density function (PDF) using a controlled quantum harmonic oscillator.
Main Methods:
- Utilizing a quantum harmonic oscillator perturbed by an electric field.
- Employing a stochastic gradient algorithm for the control electric field adaptation.
- Applying perturbation theory for statistical performance analysis.
Main Results:
- Successfully generated time-varying wave functions by controlling the electric field.
- The modulus square of the wave function tracked a given PDF.
- Analyzed control electric field dynamics and statistical performance.
Conclusions:
- A novel QNN approach enables precise control over quantum harmonic oscillators.
- This method allows for the synthesis of target probability density functions.
- Potential applications include data compression and PDF synthesis (e.g., EEG from speech).
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