Learning Gradient Boosting Ground States for Quantum Many-Body Systems

In the last few years, within the field of computational physics, there has been an upswing in the use of artificial neural networks (ANNs) as base models to build variational wave functions. These have proven to be very useful in studying quantum many-body physics, where they have successfully described the physics of those systems through the so-called neural quantum states (NQSs). However, these novel methods have focused on using mainly the ANNs, leaving away possible alternatives that can be very useful in studying physical systems. One of those alternatives is gradient boosting (GB), particularly its version with decision trees, usually called gradient-boosted trees (GBT). Due to its characteristics, it has outperformed ANNs in several machine learning competitions. Motivated by the rise of this method in various fields of data science and machine learning in general, we show in this work how the GBT method can be used together with the variational Monte Carlo framework to describe the ground state of quantum many-body systems. Furthermore, we discuss how the nature of the decision trees can be used to efficiently subdivide the Hilbert space of a quantum system and how the symmetries of the physical system under study can be used to refine our method even further.