Localization of quantum walks with classical randomness: Comparison between manual methods and supervised machine...

Area of Science:

• Quantum physics
• Machine learning
• Complex systems

Background:

• Quantum walks exhibit unique probability distributions.
• Classical randomness can influence quantum phenomena.
• Machine learning is increasingly applied to analyze physical systems.

Purpose of the Study:

• To investigate the effect of classical randomness on quantum walk probability distributions.
• To establish the generality of quantum walk localization under random perturbations.
• To compare manual analysis with supervised machine learning methods for identifying quantum phase transitions.

Main Methods:

• Simulating quantum walks with classical random rotations and translations.
• Analyzing probability distributions, momentum of inertia, and inverse participation ratio.
• Implementing and evaluating Support Vector Machines (SVM), Multilayer Perceptron (MLP), and Convolutional Neural Networks (CNN).

Main Results:

• A transition from a two-peak to a single-peak distribution occurs above a critical random parameter.
• Quantum walk localization is observed with both random rotation and translation.
• Supervised machine learning models successfully identified the transition point.
• SVM showed minor exponent underestimation; neural networks exhibited deviations with random translation.

Conclusions:

• Classical randomness can induce localization in quantum walks.
• Machine learning models demonstrate capability in detecting quantum transitions.
• Challenges remain in applying machine learning to systems with mixed quantum-classical dynamics and fluctuating distributions.