Extrapolating Quantum Observables with Machine Learning: Inferring Multiple Phase Transitions from Properties of a...

Area of Science:

• Quantum physics
• Machine learning
• Computational methods

Background:

• Predicting phase transitions in quantum systems is computationally challenging.
• Hamiltonian phase diagrams map system properties across different states.
• Current methods struggle with extrapolation into unprobed regions.

Purpose of the Study:

• To develop a machine-learning method for predicting sharp transitions in Hamiltonian phase diagrams.
• To enable extrapolation of quantum system properties across phase transition lines.
• To facilitate the search for phase transitions in experimentally or theoretically inaccessible parameter spaces.

Main Methods:

• Utilizing Gaussian process regression (GPR).
• Employing a combination of kernels selected via an iterative optimization process.
• Focusing on maximizing the predictive power of the chosen kernels.

Main Results:

• The machine-learning method successfully predicts sharp phase transitions.
• The approach demonstrates capability in extrapolating properties across transition lines.
• Predictions extend beyond adjacent phases, reaching transitions in distant parameter regions.

Conclusions:

• The developed GPR method offers a powerful tool for identifying quantum phase transitions.
• This technique significantly enhances the exploration of phase diagrams, particularly in challenging parameter regimes.
• The method holds promise for accelerating discovery in condensed matter physics and quantum computing.