Data Compression and Machine Learning for Quantum States

As an attempt to simplify the analysis of electron-hole dynamics, we make a case for the use of the Shannon Entropy as measure of the degree of entanglement of electron-hole pairs using Schmidt decomposition. The Schmidt form also allows us to determine the number of effective dimensions occupied by an arbitrary eigenstate in Hilbert space. In the case of a 50x50 diabatic density matrix for a 1-D system, we were able to reduce the number of bytes required to store this information by approximately 65% using the Schmidt form. We then reconstructed the original matrix from the reduced model and calculated values for charge transfer character and inverse participation ratio and found that the average percent error was less than 0.05% in both cases. Lastly, we demonstrate that machine learning algorithms can be used to accurately differentiate between excitonic, charge-transfer, and charge-separated states. By combining data compression and machine learning, we developed a simplified and computationally efficient way to quickly sift through thousands of eigenstates and single out relevant information about the nature of the system.