My research pursuits range from quantum information theory and machine learning to network analysis to physics education. In particular, I have developed novel approaches to characterizing entanglement in quantum systems and delineating the space of quantum states. Using recursive techniques and linear algebra, I have proved that classes of linear maps hold certain mathematical properties (positive, but not completed positive, optimal, etc.), which enabled extending so-called entanglement witnesses into high-dimensional composite systems. I have also led efforts to employ and develop the network and statistical analyses to identifying factors that affect student persistence in introductory physics courses. This work resulted in a number of surprising findings (for instance, that social integration is more important than grades in predicting persistence for certain cohorts of students) and has been highlighted in Science, Nature Physics, and as the “Editor’s Choice” in Physical Review.

In my current research, I explore the utility of machine learning algorithms and artificial intelligence, especially deep convolutional neural networks, in quantum computing platforms. At present, I am investigating methods to automatically identify stable configurations of electron spins in semiconductor-based quantum systems. I am also developing a complete software suite that enables modeling of quantum dot devices, train recognition networks, and — through mathematical optimization — auto-tune experimental setups. Success in this endeavor will eliminate the need for heuristic calibration and help scale up quantum computing into larger quantum dot arrays.

In education research, I am specifically interested in understanding what factors affect student retention and persistence in pursuing their degree. Using social network analysis, I look at the correlations between students’ overall embeddedness within the in- and out-of-class network and their odds of persistence into the second semester in a sequence. I also investigate how the attitudes toward learning with peers translate into actual behaviors. My objective is to provide a concrete basis for efforts to increase overall student retention and graduation rates at both the departmental and university levels. As part of this project, I am also developing a suite (in the R programming language) for manipulation, visualization and statistical analyses of network data.