Simulating and Learning Quantum Evolution: A CTQW-ML Framework

2025/09/13 by Soni, Rachana, Singh, Navneet Pratap
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2509.10821

Abstract

We present an approach to simulate the Schrödinger equation through continuous time quantum walks. The CTQW-based simulation applies unitary evolution driven by a quantum walk to generate probability amplitude distributions at various time steps. Additionally, we implemented a supervised neural network model to evaluate the effectiveness of data-driven techniques. The model learns to predict the squared modulus of the wavefunction given spatial and temporal coordinates. A comparative analysis demonstrates that the ML model can reproduce the qualitative structure and temporal progression of the quantum system with high accuracy. This study provides the synergy between quantum walk-based simulation and machine learning for solving quantum dynamical equations.

Citations

• Physics-informed machine learning
• Fourier Neural Operator for Parametric Partial Differential Equations
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Spatial search by quantum walk
• Exponential algorithmic speedup by a quantum walk
• Quantum Computation by Adiabatic Evolution

Related

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