Feature Engineering Is All You Need: An Overview and Analysis of Machine Learning and Algorithmic Approaches to Detecting PPT Bound Entanglement in Arbitrary Bipartite Quantum States

Abstract

The purpose of the human intellect is to identify and name the phenomena around us and manipulate them constructively. Many such phenomena have been completely classified, some with simple and methodical methods and others with algorithmic approaches. Other phenomena remain out of grasp of our ability to internalize and map their workings. Entanglement among arbitrary quantum states, particularly bound entanglement, fits into this latter type of phenomena with the possibility or impossibility of deterministically detecting this entanglement remaining an open question. Machine learning approaches have offered an unparalleled opportunity to explore previously unfeasible problems as well as expand human pattern recognition to the perfection of machine algorithms. In this work, I analyze the efficacy of 28 different machine learning methods in detecting entanglement in quantum states and compare this efficacy to that of the most advanced algorithmic approaches for this problem. In pursuit of this goal, I have produced a semi-comprehensive dataset generation and feature extraction package to benchmark entanglement detection methods. Additionally, I have implemented limited versions of two proposed algorithmic approaches in a manner feasible for modern computing capabilities. Incredibly, my results show that near-deterministic was possible for all tested splits of the data with over 90% accuracy being attained being attained for training sets as small as 50 quantum states. This high accuracy was seen even for runs with training and testing splits between bound entanglement families, implying generalizability to bound entanglement learning. Moreover, simple baseline ML methods proved to be more effective than modern high-capacity methods when feature engineering was implemented, implying that feature extraction contains most of the information relevant for classification of the dataset.