Autoregressive Generative Models for Many-body Physics

Abstract

Many body physics, the study of emergent behavior from the microscopic interactions between countless degrees of freedom, is fundamental to our understanding of the universe. Understanding these systems enable the design and development of everything from materials, pharmaceuticals and even machine learning algorithms. However, to our knowledge, classical simulation of these systems are naturally insufficient and or inefficient.

Recent developments in quantum processors herald a new age in the study of many body systems. The ability to process, extract and generalize the information from such devices is pertinent to new discoveries in the field.

In recent years, autoregressive generative models have been proven to have remarkable capabilities in a wide range of applications, from machine translation, text summarization to image generation. These models not only allow exact evaluation of the likelihood but also enable independent and identically distributed samples to be drawn from their encapsulated complex joint probability distribution of many degrees of freedom. Additionally, these models have demonstrated emergence, where the model exhibits complex behaviors allowing exceptional performance in a wide range of scenarios. These algorithms are prime candidates for the extraction of information from quantum processors and many-body systems.

In current times, data from quantum processors is still rare and expensive, as such we desire the most efficient method to extract information from such limited data. Generative models reveal themselves to be powerful tools in this scenario, achieving higher accuracies with little data.

Rich many-body systems typically inhabit higher dimensional spaces compared to the 1-dimensional sequence of autoregressive models. Consequently, a choice is required regarding the traversal of these higher dimensional systems. We explore the effects linked to this choice of traversal in the training of such models.

Furthermore, we systematically probe the generalization abilities of autoregressive generative models in a variety of axes, such as in size and parameters, for typical discrete and continuous many-body systems. Finally, Inspired by the recent establishment of correspondence between machine learning and many-body physics, we integrate real-space renormalization group into the model architecture. This integration of a many-body physics technique with machine learning demonstrates considerable promise for the future development of powerful architectures capable of achieving generality.