AI-Based Solution of Quantum Systems with Unknown Underlying Parameters

Quantum engineering is of crucial importance to the future of computing. At the heart of it is the Schrödinger equation. It is fundamental in quantum mechanics, describing the behavior of quantum systems such as the quantum harmonic oscillator. Solving such equations analytically or numerically can be challenging, particularly in the presence of noisy observations or incomplete knowledge of the system parameters. This research addresses these challenges by applying Physics-Informed Neural Networks (PINNs), an approach that integrates physical laws into machine learning frameworks. Using a fully connected feedforward neural network with dynamically weighted loss functions, we solve the Schrödinger equation for the quantum harmonic oscillator and reconstruct wavefunctions for quantum states n = 0, 1, 2 and 3. The proposed methodology balances physics loss, derived from the Schrödinger equation residual, and data loss from noisy observations. Results demonstrate excellent convergence of PINN-predicted solutions to exact wavefunctions, even in inaccurate measurements. This study contributes a robust framework for integrating physics and machine learning, with potential applications in complex quantum systems and experimental data analysis.