Characterizing Quantum Entanglement with Machine Learning
I worked on this research project with the Quantum Optics and Statics group at the University of Freiburg in my sophomore year summer. I explored different machine learning methods to discriminate high dimensional data and ultimately implemented manifold learning for entanglement states of quantum bits in quantum computers' registers. Paper here.
Manifold Learning
In UMAP manifold learning, higher dimensional data is represented in a graph with the distance between them representing how likely two points are to be connected. The algorithm optimizes the two distances (graph and lower dim distance). You can compare the two using methods such as KL divergence. After mapping the moments measured to a lower dimension, the distinct clusters are clear and classification methods like decision tree can easily sort the different classes.
Understanding the Application
Part of the challenge of this project was coming up to speed with quantum computing. Though I focused more on the ML part, I needed to understand where the data came from. Whether collected on real quantum computers or using simulators like QuTip, the data consists of randomized correlation measurements.
Results
One of the key findings is that the second moment contains the vast majority of information needed to discriminate the data. I also compared the performance of other high-dimensionality reduction methods like t-SNE and it also supports the same finding. Read more about this in the paper.