Scalable neural networks for the efficient learning of disordered quantum systems

Area of Science:

• Computational Physics
• Quantum Mechanics
• Machine Learning

Background:

• Supervised machine learning offers a computationally efficient approach for predicting complex quantum system properties.
• Deep neural networks (DNNs) show promise in learning quantum system characteristics, but their scalability with system size requires further investigation.

Purpose of the Study:

• To quantify the accuracy of DNNs in learning disordered quantum system properties as a function of system size.
• To implement and evaluate a scalable convolutional network for arbitrary system sizes.
• To compare the scalable network's performance against existing architectures and conventional dense networks.

Main Methods:

• Implementation of a scalable convolutional neural network capable of handling arbitrary system sizes.
• Training and comparison of the scalable network with an extensive convolutional architecture and dense networks.
• Predicting ground-state energies for disordered quantum systems, including cold-atom Hamiltonians and quantum Ising chains.

Main Results:

• The scalable convolutional network maintains high accuracy across various disordered quantum systems as system size increases.
• The network's scalability facilitates a transfer-learning protocol, accelerating the learning of large-system properties.
• Accurate extrapolation to system sizes beyond the training set was achieved, matching quantum Monte Carlo simulation results.

Conclusions:

• Scalable deep neural networks are effective for predicting properties of disordered quantum systems.
• Transfer learning with scalable networks significantly enhances efficiency for large quantum systems.
• This approach provides a powerful, computationally inexpensive alternative to traditional simulation methods.